killing commutative alg appendix
authorKevin Walker <kevin@canyon23.net>
Wed, 22 Sep 2010 07:26:15 -0700
changeset 553 94cadcb4831f
parent 552 c2091a3ebcc3
child 554 62d6db8c2ead
killing commutative alg appendix
blob1.tex
text/appendixes/moam.tex
text/intro.tex
--- a/blob1.tex	Tue Sep 21 22:39:17 2010 -0700
+++ b/blob1.tex	Wed Sep 22 07:26:15 2010 -0700
@@ -55,7 +55,7 @@
 
 \input{text/appendixes/comparing_defs}
 
-\input{text/comm_alg}
+%\input{text/comm_alg}
 
 % ----------------------------------------------------------------
 %\newcommand{\urlprefix}{}
--- a/text/appendixes/moam.tex	Tue Sep 21 22:39:17 2010 -0700
+++ b/text/appendixes/moam.tex	Wed Sep 22 07:26:15 2010 -0700
@@ -51,4 +51,3 @@
 Similarly, if $D^{kj}_*$ is $(k{+}i)$-acyclic then we can show that $\Compat(D^\bullet_*)$ is $i$-connected.
 \end{proof}
 
-\nn{do we also need some version of ``backwards" acyclic models?  probably}
--- a/text/intro.tex	Tue Sep 21 22:39:17 2010 -0700
+++ b/text/intro.tex	Wed Sep 22 07:26:15 2010 -0700
@@ -12,9 +12,9 @@
 \item When $n=1$ and $\cC$ is just a 1-category (e.g.\ an associative algebra), 
 the blob complex $\bc_*(S^1; \cC)$ is quasi-isomorphic to the Hochschild complex $\HC_*(\cC)$.
 (See Theorem \ref{thm:hochschild} and \S \ref{sec:hochschild}.)
-\item When $\cC$ is the polynomial algebra $k[t]$, thought of as an n-category, we have 
-that $\bc_*(M; k[t])$ is homotopy equivalent to $C_*(\Sigma^\infty(M), k)$, the singular chains
-on the configuration space of unlabeled points in $M$. (See \S \ref{sec:comm_alg}.)
+%\item When $\cC$ is the polynomial algebra $k[t]$, thought of as an n-category, we have 
+%that $\bc_*(M; k[t])$ is homotopy equivalent to $C_*(\Sigma^\infty(M), k)$, the singular chains
+%on the configuration space of unlabeled points in $M$. (See \S \ref{sec:comm_alg}.)
 \item When $\cC$ is $\pi^\infty_{\leq n}(T)$, the $A_\infty$ version of the fundamental $n$-groupoid of
 the space $T$ (Example \ref{ex:chains-of-maps-to-a-space}), 
 $\bc_*(M; \cC)$ is homotopy equivalent to $C_*(\Maps(M\to T))$,
@@ -142,8 +142,8 @@
 The appendices prove technical results about $\CH{M}$ and
 make connections between our definitions of $n$-categories and familiar definitions for $n=1$ and $n=2$, 
 as well as relating the $n=1$ case of our $A_\infty$ $n$-categories with usual $A_\infty$ algebras. 
-Appendix \ref{sec:comm_alg} describes the blob complex when $\cC$ is a commutative algebra, 
-thought of as a topological $n$-category, in terms of the topology of $M$.
+%Appendix \ref{sec:comm_alg} describes the blob complex when $\cC$ is a commutative algebra, 
+%thought of as a topological $n$-category, in terms of the topology of $M$.
 
 %%%% this is said later in the intro
 %Throughout the paper we typically prefer concrete categories (vector spaces, chain complexes)