2010/08/29 by Florin Dumitrescu, Dumitrescu, Florin · 1 citation
Mathematics · #55N99 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1008.4920
openalex publication_date 2010/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. \citeDST.