S-Structures for k-linear categories and the definition of a modular functor

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dc.creatorTillmann, Ulrike
dc.date1998-02-18
dc.date.accessioned2026-07-07T05:23:53Z
dc.date.available2026-07-07T05:23:53Z
dc.descriptionMotivated by ideas from string theory and quantum field theory new invariants of knots and 3-dimensional manifolds have been constructed from complex algebraic structures such as Hopf algebras (Reshetikhin and Turaev), monoidal categories with additional structure (Turaev and Yetter), and modular functors (Walker and Kontsevich). These constructions are very closely related. We take a unifying categorical approach based on a natural 2-dimensional generalization of a topological field theory in the sense of Atiyah and Segal, and show that the axioms defining these complex algebraic structures are a consequence of the underlying geometry of surfaces. In particular, we show that any linear category over a field with an action of the surface category is semi-simple and Artinian.
dc.descriptionAccepted for publication in the Journal of the LMS, April 1996
dc.identifierhttps://arxiv.org/abs/math/9802089
dc.identifierhttp://arxiv.org/abs/math/9802089
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76623
dc.subjectGeometric Topology
dc.subjectCategory Theory
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject57N10; 18D10; 81E05; 16A16
dc.titleS-Structures for k-linear categories and the definition of a modular functor
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