Geometric torsions and an Atiyah-style topological field theory |
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Authors: | I G Korepanov |
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Institution: | (1) South Ural State University, Chelyabinsk, Russia |
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Abstract: | We generalize the construction of invariants of three-dimensional manifolds with a triangulated boundary that we previously
proposed for the case where the boundary consists of not more than one connected component to any number of components. These
invariants are based on the torsion of acyclic complexes of geometric origin. An adequate tool for studying such invariants
turns out to be Berezin’s calculus of anticommuting variables; in particular, they are used to formulate our main theorem,
concerning the composition of invariants under a gluing of manifolds. We show that the theory satisfies a natural modification
of Atiyah’s axioms for anticommuting variables.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 405–418, March, 2009. |
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Keywords: | geometric torsion topological field theory |
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