Invariants of Spin Three-Manifolds From Chern-Simons Theory and Finite-Dimensional Hopf Algebras

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dc.creatorSawin, Stephen F.
dc.date1999-10-20
dc.date2000-05-22
dc.date.accessioned2026-07-07T05:31:14Z
dc.date.available2026-07-07T05:31:14Z
dc.descriptionA version of Kirby calculus for spin and framed three-manifolds is given and is used to construct invariants of spin and framed three-manifolds in two situations. The first is ribbon *-categories which possess odd degenerate objects. This case includes the quantum group situations corresponding to the half-integer level Chern-Simons theories conjectured to give spin TQFTs by Dijkgraaf and Witten \cite{DW90}. In particular, the spin invariants constructed by Kirby and Melvin \cite{KM91} are shown to be identical to the invariants associated to $\mathrm{SO}(3).$ Second, an invariant of spin manifolds analogous to the Hennings invariant is constructed beginning with an arbitrary factorizable, unimodular quasitriangular Hopf algebra. In particular a framed manifold invariant is associated to every finite-dimensional Hopf algebra via its quantum double, and is conjectured to be identical to Kuperberg's noninvolutory invariant of framed manifolds associated to that Hopf algebra.
dc.description39 pages of LaTeX with 15 ps figures. Various improvements as suggested by editor
dc.identifierhttps://arxiv.org/abs/math/9910106
dc.identifierhttp://arxiv.org/abs/math/9910106
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79266
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subject81T13,57N10
dc.titleInvariants of Spin Three-Manifolds From Chern-Simons Theory and Finite-Dimensional Hopf Algebras
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