Geometric torsions and invariants of manifolds with a triangulated boundary
Theoretical and mathematical physics
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
... tors undergo scalar multiplication, i.e., they work according to M. Atiyah's axioms for a topological quantum field theory.