Triangulations, categories and extended topological field theories

R.J. Lawrence

Abstract: The concept of a topological field theory is extended to encompass structures associated with manifolds of codimension >1. When all the manifolds involved are considered triangulated, it is seen that such structures may be constructed from a finite quantity of data, most conveniently viewed as associated with polyhedra and their decompositions. The special cases of 2 and 3 dimensions are briefly considered, the relations with structures of higher categories, algebras and vector spaces, becoming clear. A more detailed account is currently in preparation.

Keywords: topological field theory, higher algera structures, polyhedral decompositions, category theory

AMS subject classification: 57N15 18D05 57N10

Length: 18 pages

Reference: Quantum Topology, Eds. R. Baadhio and L.H. Kauffman, World Scientific (1993) 191-208. MR1273575 (95e:57040) (review by Sergej V. Matveev .)

Last updated on September 4th, 1996.