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This article is cited in 3 scientific papers (total 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
Citation:
I. G. Korepanov, “Geometric torsions and invariants of manifolds with a triangulated boundary”, TMF, 158:1 (2009), 98–114; Theoret. and Math. Phys., 158:1 (2009), 82–95
Linking options:
https://www.mathnet.ru/eng/tmf6301https://doi.org/10.4213/tmf6301 https://www.mathnet.ru/eng/tmf/v158/i1/p98
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Abstract page: | 456 | Full-text PDF : | 194 | References: | 73 | First page: | 6 |
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