Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Frobenius algebras and planar open string topological field theories   Motivated by the Moore-Segal axioms for an open-closed topological field
theory, we consider planar open string topological field theories. We
rigorously define a category 2Thick whose objects and morphisms can be thought
of as open strings and diffeomorphism classes of planar open string
worldsheets. Just as the category of 2-dimensional cobordisms can be described
as the free symmetric monoidal category on a commutative Frobenius algebra,
2Thick is shown to be the free monoidal category on a noncommutative Frobenius
algebra, hence justifying this choice of data in the Moore-Segal axioms. Our
formalism is inherently categorical allowing us to generalize this result. As a
stepping stone towards topological membrane theory we define a 2-category of
open strings, planar open string worldsheets, and isotopy classes of
3-dimensional membranes defined by diffeomorphisms of the open string
worldsheets. This 2-category is shown to be the free (weak monoidal) 2-category
on a `categorified Frobenius algebra', meaning that categorified Frobenius
algebras determine invariants of these 3-dimensional membranes.

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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cs