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1 %!TEX root = ../blob1.tex |
1 %!TEX root = ../blob1.tex |
2 |
2 |
3 \section{The blob complex for \texorpdfstring{$A_\infty$}{A-infinity} \texorpdfstring{$n$}{n}-categories} |
3 \section{The blob complex for \texorpdfstring{$A_\infty$}{A-infinity} \texorpdfstring{$n$}{n}-categories} |
4 \label{sec:ainfblob} |
4 \label{sec:ainfblob} |
5 Given an $A_\infty$ $n$-category $\cC$ and an $n$-manifold $M$, we make the anticlimactically tautological definition of the blob |
5 Given an $A_\infty$ $n$-category $\cC$ and an $n$-manifold $M$, we make the |
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6 anticlimactically tautological definition of the blob |
6 complex $\bc_*(M;\cC)$ to be the homotopy colimit $\cl{\cC}(M)$ of \S\ref{ss:ncat_fields}. |
7 complex $\bc_*(M;\cC)$ to be the homotopy colimit $\cl{\cC}(M)$ of \S\ref{ss:ncat_fields}. |
7 |
8 |
8 We will show below |
9 We will show below |
9 in Corollary \ref{cor:new-old} |
10 in Corollary \ref{cor:new-old} |
10 that when $\cC$ is obtained from a system of fields $\cD$ |
11 that when $\cC$ is obtained from a system of fields $\cD$ |