1 %!TEX root = ../blob1.tex |
1 %!TEX root = ../blob1.tex |
2 |
2 |
3 \section{TQFTs via fields} |
3 \section{TQFTs via fields} |
4 %\label{sec:definitions} |
4 \label{sec:fields} |
5 |
5 |
6 In this section we review the construction of TQFTs from ``topological fields". |
6 In this section we review the construction of TQFTs from ``topological fields". |
7 For more details see xxxx. |
7 For more details see \cite{kw:tqft}. |
8 |
8 |
9 We only consider compact manifolds, so if $Y \sub X$ is a closed codimension 0 |
9 We only consider compact manifolds, so if $Y \sub X$ is a closed codimension 0 |
10 submanifold of $X$, then $X \setmin Y$ implicitly means the closure |
10 submanifold of $X$, then $X \setmin Y$ implicitly means the closure |
11 $\overline{X \setmin Y}$. |
11 $\overline{X \setmin Y}$. |
12 |
12 |
13 |
13 |
14 \subsection{Systems of fields} |
14 \subsection{Systems of fields} |
15 \label{sec:fields} |
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16 |
15 |
17 Let $\cM_k$ denote the category with objects |
16 Let $\cM_k$ denote the category with objects |
18 unoriented PL manifolds of dimension |
17 unoriented PL manifolds of dimension |
19 $k$ and morphisms homeomorphisms. |
18 $k$ and morphisms homeomorphisms. |
20 (We could equally well work with a different category of manifolds --- |
19 (We could equally well work with a different category of manifolds --- |