Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On 2-dimensional topological field theories   In this paper we give a characterization of 2-dimensional topological field
theories over a space $X$ as Frobenius bundles with connections over $LX$, the
free loop space of $X$. This is a generalization of the folk theorem stating
that 2-dimensional topological field theories (over a point) are described by
finite-dimensional commutative Frobenius algebras. In another direction, this
result extends the description of 1-dimensional topological field theories over
a space $X$ as vector bundles with connections over $X$, cf. \cite{DST}.

25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th