On 2-dimensional topological field theories

Details On 2-dimensional topological field theories On 2-dimensional topological field theories

2010-08-29

arxiv.org/abs/1008.4920v1

Mathematics

Algebraic Topology

25 pages, 18 figures

Scientific paper

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}.

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