67
|
1 |
\nn{This file is obsolete.}
|
|
2 |
|
55
|
3 |
\todo{beginning of scott's attempt to write down what fields are...}
|
|
4 |
|
|
5 |
\newcommand{\manifolds}[1]{\cM_{#1}}
|
|
6 |
\newcommand{\closedManifolds}[1]{\cM_{#1}^{\text{closed}}}
|
|
7 |
\newcommand{\boundaryConditions}[1]{\cM_{#1}^{\bdy}}
|
|
8 |
Let $\manifolds{k}$ be the groupoid of manifolds (possibly with boundary) of dimension $k$ and diffeomorphisms between them. Write
|
|
9 |
$\closedManifolds{k}$ for the subgroupoid of closed manifolds. Taking the boundary gives a functor $\bdy : \manifolds{k} \to \closedManifolds{k-1}$.
|
|
10 |
Both $\manifolds{k}$ and $\closedManifolds{k}$ are symmetric tensor categories under the operation of disjoint union.
|
|
11 |
\begin{defn}
|
|
12 |
A \emph{system of fields} is a collection of functors $\cF_k$ associating a `set of fields' to each manifold of dimension at most $n$.
|
|
13 |
|
|