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Invariants of piecewise-linear 3-manifolds |
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| Authors: | John W Barrett Bruce W Westbury |
| Institution: | Department of Mathematics, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K. ; Department of Mathematics, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K. |
| Abstract: | This paper presents an algebraic framework for constructing invariants of closed oriented 3-manifolds by taking a state sum model on a triangulation. This algebraic framework consists of a tensor category with a condition on the duals which we have called a spherical category. A significant feature is that the tensor category is not required to be braided. The main examples are constructed from the categories of representations of involutive Hopf algebras and of quantised enveloping algebras at a root of unity. |
| Keywords: | 3-manifold invariants state sum model bistellar moves spherical category spherical Hopf algebra |
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