# HG changeset patch # User Kevin Walker # Date 1285165575 25200 # Node ID 94cadcb4831f149af01683fc230017a79e252b01 # Parent c2091a3ebcc359a6449674090ce2e88e1fa3dc0c killing commutative alg appendix diff -r c2091a3ebcc3 -r 94cadcb4831f blob1.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}{} diff -r c2091a3ebcc3 -r 94cadcb4831f text/appendixes/moam.tex --- 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} diff -r c2091a3ebcc3 -r 94cadcb4831f text/intro.tex --- 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)