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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
MathSciNet review: 1357878
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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: http://dx.doi.org/10.1090/S0002-9947-96-01660-1
PII: S 0002-9947(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