Mathematics – Geometric Topology
Scientific paper
2008-06-16
Theor.Math.Phys.158:344-354,2009
Mathematics
Geometric Topology
15 pages, English translation (with minor corrections) of the Russian version. The latter is avaible here as v1
Scientific paper
10.1007/s11232-009-0028-0
The construction of invariants of three-dimensional manifolds with a triangulated boundary, proposed earlier by the author for the case when the boundary consists of not more than one connected component, is generalized to any number of components. These invariants are based on the torsion of acyclic complexes of geometric origin. The relevant tool for studying our invariants turns out to be F.A. Berezin's calculus of anti-commuting variables; in particular, they are used in the formulation of the main theorem of the paper, concerning the composition of invariants under a gluing of manifolds. We show that the theory obeys a natural modification of M. Atiyah's axioms for anti-commuting variables.
Korepanov Igor
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