Geometric torsions and invariants of manifolds with a triangulated boundary |
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Authors: | I. G. Korepanov |
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Affiliation: | (1) South Ural State University, Chelyabinsk, Russia |
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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. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 1, pp. 98–114, January, 2009. |
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Keywords: | topological quantum field theory Atiyah’ s axioms geometric acyclic complex |
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