preface.tex

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\section*{Preface}
Over the 2016--2017 academic year, I ran the standard algebraic topology 
sequence at MIT. The first semester deals with singular homology and 
cohomology, and Poicar\'e duality; the second builds up basic homotopy theory,
spectral sequences, and characteristic classes. 

I was lucky enough to have in the audience a student, Sanath Devalapurkar, 
who spontaneously decided to live\TeX \ the entire course. This resulted in 
a remarkably accurate record of what happened in the classroom -- right down
to random alarms ringing and embarassing mistakes on the blackboard. 
Sanath's \TeX \ forms the basis of these notes. 

My goal was to give a standard classical approach to these subjects. 
In the first semester, I tried to give an honest account of the relative cup
products needed in the proof of Poincar\'e duality. 

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%\section*{Preface}
%These are notes from the 18.905-906 sequence, taught by Haynes Miller in the
%academic year 2016-2017. The goal was to tell the story of classical algebraic
%topology, starting from the basics of homology and cohomology, all the way up
%to the Serre spectral sequence and characteristic classes. I tried to live\TeX
%the entire course. As such, there are multiple typos and mathematical errors,
%which I am terribly ashamed of.
%
%Haynes, a few other students from the class, and I are working to clean (and,
%in extreme cases, rewrite) the exposition in some chapters. Hopefully this
%project will be completed by the first month of 2018, in time for the second
%run of 18.906.
%
%I'd appreciate any input on where these notes can be fixed. The github
%repository for the project is at
%\begin{center}
%    \url{https://github.com/sanathdevalapurkar/algtop-notes}.
%\end{center}
%Any comments can be sent to \verb|sanathd@mit.edu|.
%
%--- Sanath
%
%\newpage
%%Here are hyperlinks to the notes from each of the semesters.
%%    \begin{enumerate}
%%        \item The notes for 18.905 start at section \ref{905}.
%%        \item The notes for 18.906 start at section \ref{906}.
%%    \end{enumerate}
%
%%\section*{Stuff to fix}
%%\begin{itemize}
%%    \item The original version of the notes used
%%	\verb|\cc| to denote both a script C and the complex numbers.
%%	Now, \verb|\cc| denotes a script C and \verb|\cC| denotes the complex
%%	numbers.
%%	Everytime you find this, edit it!
%%    \item Be consistent about your use of $\Hom_\cc(C,D)$ and $\cc(C,D)$ for hom-sets.
%%\end{itemize}
%
%\section*{Things to fix}
%\begin{itemize}
%    \item As of \today, all of Part II has been edited, with the exception of
%	\S \ref{basepoints}, \S \ref{section-serre-classes}, \S
%	\ref{mod-c-hurewicz}, \S \ref{dress-sseq}, \S \ref{leray-hirsch}, and
%	\S \ref{gysin-sequence}.
%    \item Part I remains to be edited.
%    \item The original version of the notes used \verb|\cc| to denote both a
%	script C and the complex numbers.  Now, \verb|\cc| denotes a script C
%	and \verb|\cC| denotes the complex numbers. This is a problem that
%	needs to be fixed everywhere.
%\end{itemize}