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TMF, 2009, Volume 158, Number 3, Pages 405–418 (Mi tmf6323)  

This article is cited in 4 scientific papers (total in 4 papers)

Geometric torsions and an Atiyah-style topological field theory

I. G. Korepanov

South Ural State University

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.

Keywords: geometric torsion, topological field theory

DOI: https://doi.org/10.4213/tmf6323

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English version:
Theoretical and Mathematical Physics, 2009, 158:3, 344–354

Bibliographic databases:

Received: 15.06.2008

Citation: I. G. Korepanov, “Geometric torsions and an Atiyah-style topological field theory”, TMF, 158:3 (2009), 405–418; Theoret. and Math. Phys., 158:3 (2009), 344–354

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf6323
  • https://doi.org/10.4213/tmf6323
  • http://mi.mathnet.ru/eng/tmf/v158/i3/p405

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. I. Bel'kov, I. G. Korepanov, “A matrix solution of the pentagon equation with anticommuting variables”, Theoret. and Math. Phys., 163:3 (2010), 819–830  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. Igor G. Korepanov, Nurlan M. Sadykov, “Parameterizing the Simplest Grassmann–Gaussian Relations for Pachner Move 3–3”, SIGMA, 9 (2013), 053, 19 pp.  mathnet  crossref  mathscinet
    3. Korepanov I.G., “Two-Cocycles Give a Full Nonlinear Parameterization of the Simplest 3-3 Relation”, Lett. Math. Phys., 104:10 (2014), 1235–1261  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. I. G. Korepanov, D. V. Talalaev, G. I. Sharygin, “Integrable 3D statistical models on six-valent graphs”, Proc. Steklov Inst. Math., 302 (2018), 198–216  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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