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.
- Pub Date:
- November 1993
- High Energy Physics - Theory;
- Mathematics - Quantum Algebra
- 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