Invariants of piecewise-linear 3-manifolds

Barrett, John; Westbury, Bruce

doi:10.1090/S0002-9947-96-01660-1

Invariants of piecewise-linear 3-manifolds
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by John W. Barrett and Bruce W. Westbury PDF

Trans. Amer. Math. Soc. 348 (1996), 3997-4022 Request permission

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.

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