Twin TQFTs and Frobenius algebras

Details Twin TQFTs and Frobenius algebras Twin TQFTs and Frobenius algebras

2009-01-20

arxiv.org/abs/0901.2979v3

Mathematics

Geometric Topology

38 pages, many figures; some concepts have been clarified; references and proofs have been added

Scientific paper

We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on a twin Frobenius algebra, by providing a description of this category in terms of generators and relations. A twin Frobenius algebra (C, W, z, z^*) consists of a commutative Frobenius algebra C, a symmetric Frobenius algebra W, and an algebra homomorphism z: C - > W with dual z^*: W -> C, satisfying some extra conditions. We also introduce a generalized 2-dimensional Topological Quantum Field Theory defined on singular 2-dimensional cobordisms and show that it is equivalent to a twin Frobenius algebra in a symmetric monoidal category.

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