Invariants of piecewise-linear 3-manifolds

Authors:
John W. Barrett and Bruce W. Westbury

Journal:
Trans. Amer. Math. Soc. **348** (1996), 3997-4022

MSC (1991):
Primary 57N10

DOI:
https://doi.org/10.1090/S0002-9947-96-01660-1

MathSciNet review:
1357878

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**John W. Barrett**

Affiliation:
Department of Mathematics, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K.

Email:
jwb@maths.nott.ac.uk

**Bruce W. Westbury**

Affiliation:
Department of Mathematics, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K.

Email:
bww@maths.nott.ac.uk

DOI:
https://doi.org/10.1090/S0002-9947-96-01660-1

Keywords:
3-manifold invariants,
state sum model,
bistellar moves,
spherical category,
spherical Hopf algebra

Received by editor(s):
July 20, 1994

Article copyright:
© Copyright 1996
American Mathematical Society