Geodesic
Geometric torsions and invariants of manifolds with a triangulated boundary
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 1, pp. 98-114
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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. 
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I. G. Korepanov. Geometric torsions and invariants of manifolds with a triangulated boundary. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 1, pp. 98-114. http://geodesic.mathdoc.fr/item/TMF_2009_158_1_a5/

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