This article is cited in 2 scientific papers (total in 2 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
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.
virtual manifolds, $3$-manifolds, hyperbolic manifolds, complexity.
|Ministry of Education and Science of the Russian Federation
|Russian Foundation for Basic Research
|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).
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Sbornik: Mathematics, 2016, 207:11, 1493–1511
MSC: Primary 57M99; Secondary 57M20
A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Complexity of virtual 3-manifolds”, Mat. Sb., 207:11 (2016), 4–24; Sb. Math., 207:11 (2016), 1493–1511
Citation in format AMSBIB
\by A.~Yu.~Vesnin, V.~G.~Turaev, E.~A.~Fominykh
\paper Complexity of virtual 3-manifolds
\jour Mat. Sb.
\jour Sb. Math.
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E. A. Sbrodova, V. V. Tarkaev, E. A. Fominykh, E. V. Shumakova, “Virtualnye trekhmernye mnogoobraziya slozhnosti $1$ i $2$”, Tr. IMM UrO RAN, 23, no. 4, 2017, 257–264
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
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