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Lecture already delivered - adding to version control for later use. These notes rely heavily on sources referenced in main.tex
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‎bin/ext.pdf

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‎makefile

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OUT_NAME = ext
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OUT_DIR = ./bin/
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TEX_MAIN = ./src/main.tex
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TEXCC = pdflatex
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CCFLAGS = -jobname=$(OUT_NAME) -output-dir=$(OUT_DIR) -interaction=nonstopmode
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.PHONY: all clean
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all: $(OUT_DIR) $(OUT_NAME)
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$(OUT_NAME):
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$(TEXCC) $(CCFLAGS) $(TEX_MAIN)
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$(OUT_DIR):
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mkdir $@
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clean:
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rm $(OUT_DIR)*

‎src/header.tex

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%% LaTeX header file for Math 821, Algebraic Topology
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%% JLM 1/9/18
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%% Feel free to use or modify these macros as you see fit.
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% General stuff
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\documentclass[reqno]{amsart}
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\usepackage{amssymb,amsmath,amsthm,graphics,hyperref,mathrsfs,stmaryrd,dsfont,youngtab,tcolorbox,framed,blkarray,color,fullpage}
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\usepackage[all]{xy}
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\usepackage{enumerate}
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\usepackage{bbm}
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\numberwithin{equation}{section}
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\renewcommand{\phi}{\varphi}
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%%%%%%%%%%%%%%%% Macros for figures %%%%%%%%%%%%%%%%
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%% I like to keep all my figures in a subfolder called "figs". If you keep figures in the same folder as the source .tex tile, remove "figs/" from the macros.
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%% Usage: \includefigure{height}{width}{filename}
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\newcommand{\includefigure}[3]{{
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\begin{center}
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\resizebox{#1}{#2}{\includegraphics{{figs/#3}}}
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\end{center}}}
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\newcommand{\includefigurewithinmath}[3]{{
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\resizebox{#1}{#2}{\includegraphics{{figs/#3}}}}}
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%%%%%%%%%%%%%%%% Vertical spacing %%%%%%%%%%%%%%%%
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\newcommand{\hugepad}{\rule[-14mm]{0mm}{30mm}}
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\newcommand{\bigpad}{\rule[-5mm]{0mm}{15mm}}
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\newcommand{\bigpadup}{\rule{0mm}{10mm}}
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\newcommand{\bigpaddown}{\rule[-5mm]{0mm}{5mm}}
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\newcommand{\smallpad}{\rule[-1.5mm]{0mm}{5mm}}
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\newcommand{\pad}{\rule[-3mm]{0mm}{8mm}}
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\newcommand{\padup}{\rule{0mm}{5mm}}
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\newcommand{\paddown}{\rule[-3mm]{0mm}{2mm}}
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\newcommand{\blank}{\rule{1.25in}{0.25mm}}
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\newcommand{\yell}[1]{\begin{framed}{#1}\end{framed}}
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\newcommand{\bang}{$\bullet$\quad}
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\newcommand{\indnt}{\phantom{.}\qquad}
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\newcommand{\littleline}{\begin{center}\rule{4in}{0.5bp}\end{center}}
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\newcommand{\defterm}[1]{\boldmath\textbf{#1}\unboldmath}
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\newcommand{\icol}[1]{% inline column vector
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\left(\begin{smallmatrix}#1\end{smallmatrix}\right)%
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}
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%%%%%%%%%%%%%%%% Colors for TikZ and text %%%%%%%%%%%%%%%%%
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\definecolor{light}{gray}{.75}
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\definecolor{med}{gray}{.5}
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\definecolor{dark}{gray}{.25}
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\newcommand{\Red}[1]{{\color{red}{#1}}}
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\newcommand{\RED}[1]{{\color{red}{\boldmath\textbf{#1}\unboldmath}}}
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\newcommand{\Blue}[1]{{\color{blue}{#1}}}
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\newcommand{\BLUE}[1]{{\color{blue}{\boldmath\textbf{#1}\unboldmath}}}
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%%%%%%%%%%%%%%%%%%%% Hyperlinks %%%%%%%%%%%%%%%%%%%%
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\newcommand{\hreftext}[2]{\href{#1}{\Blue{#2}}}
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\newcommand{\hrefurl}[2]{\href{#1}{\Blue{\tt #2}}}
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%%%%%%%%%%%%%%%%%%%% Math operators %%%%%%%%%%%%%%%%%%%%
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\DeclareMathOperator{\Spec}{Spec}
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\DeclareMathOperator{\interior}{Int}
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\DeclareMathOperator{\Mod}{Mod}
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\newcommand{\etale}{\'etal{e\xspace}}
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\DeclareMathOperator{\Ab}{Ab}
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\DeclareMathOperator{\coker}{coker}
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\DeclareMathOperator{\Comm}{Comm}
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\DeclareMathOperator{\conv}{conv}
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\DeclareMathOperator{\diag}{diag}
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\DeclareMathOperator{\Ext}{Ext}
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\DeclareMathOperator{\Gr}{Gr}
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\DeclareMathOperator{\Hom}{Hom}
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\DeclareMathOperator{\im}{im}
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\DeclareMathOperator{\Link}{link}
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\DeclareMathOperator{\nullspace}{nullspace}
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\DeclareMathOperator{\Poin}{Poin}
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\DeclareMathOperator{\rank}{rank}
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\DeclareMathOperator{\rel}{rel}
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\DeclareMathOperator{\Tor}{Tor}
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\DeclareMathOperator{\tr}{tr}
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\DeclareMathOperator{\sd}{sd}
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\DeclareMathOperator{\Star}{star}
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\DeclareMathOperator{\support}{support}
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\DeclareMathOperator{\vol}{vol}
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%%%%%%%%%%%%%%%%%%%% Theorem environments with automatic numbering
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\newtheorem{theorem}{Theorem}[section]
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\newtheorem{proposition}[theorem]{Proposition}
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{criterion}[theorem]{Criterion}
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\theoremstyle{definition}
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\newtheorem{definition}[theorem]{Definition}
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\newtheorem{example}[theorem]{Example}
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\newtheorem{remark}[theorem]{Remark}
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\newtheorem{problem}[theorem]{Problem}
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\theoremstyle{remark}
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\newtheorem{exercise}{Exercise}
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%%%%%%%%%%%%%%%%%%%% Unnumbered theorem proclamations
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\newcommand{\cor}{{\bf Corollary: }}
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\newcommand{\defn}{{\bf Definition: }}
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\newcommand{\defnthm}{{\bf Definition/Theorem: }}
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\newcommand{\defnprop}{{\bf Definition/Proposition: }}
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\newcommand{\defns}{{\bf Definitions: }}
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\newcommand{\exa}{{\bf Example: }}
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\newcommand{\fact}{{\bf Fact: }}
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\newcommand{\lem}{{\bf Lemma: }}
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\newcommand{\notn}{{\bf Notation: }}
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\newcommand{\obs}{{\bf Observation: }}
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\newcommand{\note}{{\bf Note: }}
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\newcommand{\prop}{{\bf Proposition: }}
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\newcommand{\rmk}{{\bf Remark: }}
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\newcommand{\skpr}{\emph{Sketch of proof: }}
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\newcommand{\soln}{{\bf Solution: }}
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\newcommand{\altsoln}{{\bf Alternate Solution: }}
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\newcommand{\altaltsoln}{{\bf Another Alternate Solution: }}
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\newcommand{\thm}{{\bf Theorem: }}
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\newcommand{\half}{\frac{1}{2}}
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\newcommand{\thalf}{\tfrac{1}{2}}
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\newcommand{\dhalf}{\dfrac{1}{2}}
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\newcommand{\0}{\emptyset}
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\newcommand{\bd}{\partial} %% boundary
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\newcommand{\dju}{\ensuremath{\mathaccent\cdot\cup}} %% disjoint union
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\newcommand{\eqdef}{\overset{\rm def}{=}}
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\newcommand{\ergo}{\therefore} %% just because it's shorter
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\newcommand{\excise}[1]{} % for commenting out large blocks of LaTeX source
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\newcommand{\intersection}{\cap}
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\newcommand{\isom}{\cong} %% homeomorphism
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\newcommand{\htop}{\simeq} %% homotopy equivalence
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\newcommand{\ov}[1]{\overline{{#1}}}
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\newcommand{\qandq}{\quad\text{and}\quad}
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\newcommand{\qqandqq}{\qquad\text{and}\qquad}
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\newcommand{\qand}{\quad\text{and}}
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\newcommand{\ray}{\overrightarrow}
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\newcommand{\rchi}{\raisebox{0.05cm}{\ensuremath{\chi}}} %% because chi looks funny otherwise
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\newcommand{\sm}{\setminus}
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\newcommand{\st}{~|~} %% ``such that''
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\newcommand{\www}{\mathsf w} %% winding number
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\newcommand{\x}{\times}
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\newcommand{\union}{\cup}
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\newcommand{\zerovec}{\mathbf{0}}
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%% Arrows
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\newcommand{\into}{\hookrightarrow} % injection
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\newcommand{\onto}{\twoheadrightarrow} % surjection
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\newcommand{\inj}{\hookrightarrow} % injection
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\newcommand{\surj}{\twoheadrightarrow} % surjection
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%% Arrows for use with xy
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\newcommand{\rto}{\ar[r]}
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\newcommand{\rrto}{\ar[rr]}
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\newcommand{\lto}{\ar[l]}
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\newcommand{\llto}{\ar[ll]}
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\newcommand{\uto}{\ar[u]}
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\newcommand{\uuto}{\ar[uu]}
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\newcommand{\dto}{\ar[d]}
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\newcommand{\ddto}{\ar[dd]}
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\newcommand{\dlto}{\ar[dl]}
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\newcommand{\drto}{\ar[dr]}
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\newcommand{\ulto}{\ar[ul]}
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\newcommand{\urto}{\ar[ur]}
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\newcommand{\ddlto}{\ar[ddl]}
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\newcommand{\dllto}{\ar[dll]}
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\newcommand{\ddrto}{\ar[ddr]}
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\newcommand{\drrto}{\ar[drr]}
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\newcommand{\uulto}{\ar[uul]}
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\newcommand{\ullto}{\ar[ull]}
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\newcommand{\uurto}{\ar[uur]}
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\newcommand{\urrto}{\ar[urr]}
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\newcommand{\ddllto}{\ar[ddll]}
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\newcommand{\uullto}{\ar[uull]}
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%% Straight lines for use with xy
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\newcommand{\rlineto}{\ar@{-}[r]}
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\newcommand{\rrlineto}{\ar@{-}[rr]}
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\newcommand{\llineto}{\ar@{-}[l]}
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\newcommand{\lllineto}{\ar@{-}[ll]}
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\newcommand{\ulineto}{\ar@{-}[u]}
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\newcommand{\uulineto}{\ar@{-}[uu]}
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\newcommand{\dlineto}{\ar@{-}[d]}
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\newcommand{\ddlineto}{\ar@{-}[dd]}
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\newcommand{\dllineto}{\ar@{-}[dl]}
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\newcommand{\drlineto}{\ar@{-}[dr]}
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\newcommand{\ullineto}{\ar@{-}[ul]}
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\newcommand{\urlineto}{\ar@{-}[ur]}
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\newcommand{\ddllineto}{\ar@{-}[ddl]}
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\newcommand{\dlllineto}{\ar@{-}[dll]}
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\newcommand{\ddrlineto}{\ar@{-}[ddr]}
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\newcommand{\drrlineto}{\ar@{-}[drr]}
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\newcommand{\uullineto}{\ar@{-}[uul]}
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\newcommand{\ulllineto}{\ar@{-}[ull]}
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\newcommand{\uurlineto}{\ar@{-}[uur]}
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\newcommand{\urrlineto}{\ar@{-}[urr]}
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%% Boldface letters
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\renewcommand{\aa}{\mathbf{a}}
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\newcommand{\bb}{\mathbf{b}}
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\newcommand{\pp}{\mathbf{p}}
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\newcommand{\qq}{\mathbf{q}}
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\newcommand{\vv}{\mathbf{v}}
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\newcommand{\ww}{\mathbf{w}}
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\newcommand{\xx}{\mathbf{x}}
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\newcommand{\yy}{\mathbf{y}}
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\newcommand{\zz}{\mathbf{z}}
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%% Calligraphic letters
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\newcommand{\A}{\mathcal{A}}
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\newcommand{\B}{\mathcal{B}}
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\newcommand{\C}{\mathcal{C}}
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\newcommand{\M}{\mathcal{M}}
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\renewcommand{\P}{\mathcal{P}}
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\newcommand{\T}{\mathcal{T}}
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%% Fancy script letters
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\newcommand{\BB}{\mathscr{B}}
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\newcommand{\CC}{\mathscr{C}}
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\newcommand{\FF}{\mathscr{F}}
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\newcommand{\II}{\mathscr{I}}
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\newcommand{\LL}{\mathscr{L}}
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\newcommand{\PP}{\mathscr{P}}
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\renewcommand{\SS}{\mathscr{S}}
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\newcommand{\TT}{\mathscr{T}}
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\newcommand{\XX}{\mathscr{X}}
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%% Blackboard bold letters
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\newcommand{\Aa}{\mathbb{A}}
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\newcommand{\Cc}{\mathbb{C}}
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\newcommand{\Ff}{\mathbb{F}}
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\newcommand{\Nn}{\mathbb{N}}
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\newcommand{\Pp}{\mathbb{P}}
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\newcommand{\Qq}{\mathbb{Q}}
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\newcommand{\Rr}{\mathbb{R}}
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\newcommand{\Ss}{\mathbb{S}}
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\newcommand{\Zz}{\mathbb{Z}}
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\newcommand{\IdMap}{\mathds{1}}
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\newcommand{\RP}{\Rr P}
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\newcommand{\CP}{\Cc P}
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\newcommand{\RPN}{\Rr P^n}
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\newcommand{\CPN}{\Cc P^n}
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\newcommand{\RPn}{\Rr P^n}
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\newcommand{\CPn}{\Cc P^n}
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%% tilde H for reduced homology
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\newcommand{\HH}{\tilde H}
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%% big double angle brackets
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\newcommand{\Langle}{\big\langle\!\!\big\langle}
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\newcommand{\Rangle}{\big\rangle\!\!\big\rangle}
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%% macros for automatic problem numbering
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\newcounter{probno}
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\setcounter{probno}{0}
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\newcounter{partno}
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\setcounter{partno}{0}
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%% versions that don't print the number of points
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\newcommand{\yellprob}[1]{%
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\bigskip\begin{framed}
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\setcounter{partno}{0}%
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\addtocounter{probno}{1}%
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{\bf Problem~\#{\arabic{probno}}}\quad\bf\boldmath #1\unboldmath
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\end{framed}}
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\newcommand{\yellprobpart}[1]{
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\bigskip\begin{framed}%
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\addtocounter{partno}{1}%
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{\bf (\#\arabic{probno}\alph{partno})}\ \ \bf\boldmath #1\unboldmath
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\end{framed}}
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\newcommand{\prob}{
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\vskip10bp%
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\setcounter{partno}{0}%
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\addtocounter{probno}{1}%
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{\bf Problem~\#{\arabic{probno}}}\quad}
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\newcommand{\probpart}{%\rule{0in}{0in}\\ \phantom{xxx}
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\addtocounter{partno}{1}%
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{\bf (\#\arabic{probno}\alph{partno})}\ \ }
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\newcommand{\probcont}{%
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{\bf Problem~\#{\arabic{probno}}}~(\emph{continued})}
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\newcommand{\probo}{
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\setcounter{partno}{0}%
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\addtocounter{probno}{1}%
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{\bf (\#\arabic{probno})}\ \ }
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\newcommand{\abs}[1] {
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\left| #1 \right|}

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