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1 %!TEX root = ../blob1.tex |
1 %!TEX root = ../blob1.tex |
2 \nn{Not sure where this goes yet: small blobs, unfinished:} |
2 \nn{Not sure where this goes yet: small blobs, unfinished:} |
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3 |
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4 % ******* temporary |
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5 \def\setc#1#2{\{#1|#2\}} |
3 |
6 |
4 Fix $\cU$, an open cover of $M$. Define the `small blob complex' $\bc^{\cU}_*(M)$ to be the subcomplex of $\bc_*(M)$ of all blob diagrams in which every blob is contained in some open set of $\cU$. |
7 Fix $\cU$, an open cover of $M$. Define the `small blob complex' $\bc^{\cU}_*(M)$ to be the subcomplex of $\bc_*(M)$ of all blob diagrams in which every blob is contained in some open set of $\cU$. |
5 |
8 |
6 \begin{lem}[Small blobs] |
9 \begin{lem}[Small blobs] |
7 The inclusion $i: \bc^{\cU}_*(M) \into \bc_*(M)$ is a homotopy equivalence. |
10 The inclusion $i: \bc^{\cU}_*(M) \into \bc_*(M)$ is a homotopy equivalence. |