Geometric torsions and invariants of manifolds with triangulated boundary

Details Geometric torsions and invariants of manifolds with triangulated boundary Geometric torsions and invariants of manifolds with triangulated boundary

2008-03-02

arxiv.org/abs/0803.0123v1

Theor. Math. Phys. 158:1 (2009) 82-95

Mathematics

Geometric Topology

18 pages, 4 figures

Scientific paper

10.1007/s11232-009-0006-6

Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a manifold with a triangulated boundary. These invariants can be naturally united in a vector, and a change of the boundary triangulation corresponds to a linear transformation of this vector. Moreover, when two manifolds are glued by their common boundary, these vectors undergo scalar multiplication, i.e., they work according to M. Atiyah's axioms for a topological quantum field theory.

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