Frobenius algebras and planar open string topological field theories

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dc.creatorLauda, Aaron D.
dc.date2005-08-18
dc.date.accessioned2026-07-07T05:22:29Z
dc.date.available2026-07-07T05:22:29Z
dc.descriptionMotivated 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.
dc.description66 pages, diagrams in xypic and pstricks
dc.identifierhttps://arxiv.org/abs/math/0508349
dc.identifierhttp://arxiv.org/abs/math/0508349
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76076
dc.subjectQuantum Algebra
dc.subjectGeometric Topology
dc.subject57R56;18D05;57M99
dc.titleFrobenius algebras and planar open string topological field theories
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