This article is cited in 3 papers

Geometric torsions and invariants of manifolds with a triangulated boundary

I. G. Korepanov

South Ural State University

Abstract: Geometric torsions are torsions of acyclic complexes of vector spaces consisting of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a three-dimensional manifold with a triangulated boundary. These invariants can be naturally combined into a vector, and a change of the boundary triangulation corresponds to a linear transformation of this vector. Moreover, when two manifolds are glued at their common boundary, these vectors undergo scalar multiplication, i.e., they satisfy Atiyah's axioms of a topological quantum field theory.

Keywords: topological quantum field theory, Atiyah's axioms, geometric acyclic complex.

Received: 21.02.2008

DOI: 10.4213/tmf6301

 English version: Theoretical and Mathematical Physics, 2009, 158:1, 82–95

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