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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 138, Number 1, Pages 23–34
DOI: https://doi.org/10.4213/tmf11 (Mi tmf11) 		 
This article is cited in 6 scientific papers (total in 6 papers)

$SL(2)$-Solution of the Pentagon Equation and Invariants of Three-Dimensional Manifolds

I. G. Korepanov

South Ural State University
Full-text PDF (226 kB) Citations (6)
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DOI: https://doi.org/10.4213/tmf11
Abstract: We construct an algebraic complex corresponding to a triangulation of a three-manifold starting with a classical solution of the pentagon equation, constructed earlier by the author and Martyushev and related to the flat geometry, which is invariant under the group $SL(2)$. If this complex is acyclic (which is confirmed by examples), we can use it to construct an invariant of the manifold.
Keywords: pentagon equation, Pachner moves, acyclic complexes, torsion, invariants of manifolds.
Received: 23.12.2002
English version:
Theoretical and Mathematical Physics, 2004, Volume 138, Issue 1, Pages 18–27
DOI: https://doi.org/10.1023/B:TAMP.0000010629.96356.52
Bibliographic databases:
Language: Russian
Citation: I. G. Korepanov, “$SL(2)$-Solution of the Pentagon Equation and Invariants of Three-Dimensional Manifolds”, TMF, 138:1 (2004), 23–34; Theoret. and Math. Phys., 138:1 (2004), 18–27
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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