Invariants of Piecewise-Linear 3-Manifolds

Abstract

In this paper we develop a theory for constructing an invariant of closed oriented 3-manifolds, given a certain type of Hopf algebra. Examples are given by a quantised enveloping algebra of a semisimple Lie algebra, or by a semisimple involutory Hopf algebra. The invariant is defined by a state sum model on a triangulation. In some cases, the invariant is the partition function of a topological quantum field theory.

30 pages, with postscript figures. Manuscript slightly revised to version of 24 June 1994, and TeX standardised to eliminate the use of non-standard macros or fonts

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