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

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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)

S L (2)

$SL(2)$ -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

S L (2)

$SL(2)$ . 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, “

S L (2)

$SL(2)$ -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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https://www.mathnet.ru/eng/tmf11

https://doi.org/10.4213/tmf11

https://www.mathnet.ru/eng/tmf/v138/i1/p23

This publication is cited in the following 6 articles:

V. O. Manturov, I. M. Nikonov, “On an Invariant of Pure Braids”, Dokl. Math., 109:2 (2024), 164
V. O. Manturov, I. M. Nikonov, “On an invariant of pure braids”, Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, 516 (2024), 79
Vassily Olegovich Manturov, Zheyan Wan, “The photography method: Solving pentagon equation”, J. Knot Theory Ramifications, 32:11 (2023)
Aristophanes Dimakis, Folkert Müller-Hoissen, “Simplex and Polygon Equations”, SIGMA, 11 (2015), 042, 49 pp.
I. G. Korepanov, “Geometric torsions and an Atiyah-style topological field theory”, Theoret. and Math. Phys., 158:3 (2009), 344–354
Igor G. Korepanov, “Pachner Move $3\to 3$ and Affine Volume-Preserving Geometry in $\mathbb R^3$ ”, SIGMA, 1 (2005), 021, 7 pp.

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

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Abstract page:	411
Full-text PDF :	203
References:	51
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