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Sbornik: Mathematics, 2016, Volume 207, Issue 11, Pages 1493–1511
DOI: https://doi.org/10.1070/SM8700 (Mi sm8700) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Complexity of virtual 3-manifolds

A. Yu. Vesninab, V. G. Turaevcb, E. A. Fominykhbd

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Chelyabinsk State University
c Indiana University, Bloomington, IN, USA
d Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
English version PDF (551 kB) Citations (3) Russian version article
References:
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DOI: https://doi.org/10.1070/SM8700
Abstract: Virtual $3$-manifolds were introduced by Matveev in 2009 as natural generalizations of classical $3$-manifolds. In this paper, we introduce a notion of complexity for a virtual $3$-manifold. We investigate the values of the complexity for virtual 3-manifolds presented by special polyhedra with one or two $2$-components. On the basis of these results, we establish the exact values of the complexity for a wide class of hyperbolic $3$-manifolds with totally geodesic boundary.
Bibliography: 24 titles.
Keywords: virtual manifolds, $3$-manifolds, hyperbolic manifolds, complexity.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.Z50.31.0020
1.1260.2014/K
Russian Foundation for Basic Research 16-01-00609-a
This work was supported by the Laboratory of Quantum Topology, Chelyabinsk State University (grant no. 14.Z50.31.0020 of the government of the Russian Federation). A. Yu. Vesnin and E. A. Fominykh were also supported in part by the Russian Foundation for Basic Research (grant no. 16-01-00609-a), and by the Ministry of Education and Science of the Russian Federation (state task no. 1.1260.2014/K).
Received: 20.03.2016
Bibliographic databases:
Document Type: Article
UDC: 515.16
MSC: Primary 57M99; Secondary 57M20
Language: English
Original paper language: Russian
Citation: A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Complexity of virtual 3-manifolds”, Sb. Math., 207:11 (2016), 1493–1511
Citation in format AMSBIB
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\by A.~Yu.~Vesnin, V.~G.~Turaev, E.~A.~Fominykh
\paper Complexity of virtual 3-manifolds
\jour Sb. Math.
\yr 2016
\vol 207
\issue 11
\pages 1493--1511
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\crossref{https://doi.org/10.1070/SM8700}
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  • https://www.mathnet.ru/eng/sm8700
  • https://doi.org/10.1070/SM8700
  • https://www.mathnet.ru/eng/sm/v207/i11/p4
    • This publication is cited in the following 3 articles:
    1. E. A. Fominykh, E. V. Shumakova, “Poor ideal three-edge triangulations are minimal”, Siberian Math. J., 62:5 (2021), 943–950  mathnet  crossref  crossref  isi  elib
    2. A. Yu. Vesnin, S. V. Matveev, E. A. Fominykh, “New aspects of complexity theory for 3-manifolds”, Russian Math. Surveys, 73:4 (2018), 615–660  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. E. A. Sbrodova, V. V. Tarkaev, E. A. Fominykh, E. V. Shumakova, “Virtual $3$-manifolds of complexity $1$ and $2$”, Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S154–S160  mathnet  crossref  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:772
    Russian version PDF:102
    English version PDF:37
    References:79
    First page:54
     
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