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Sibirsk. Mat. Zh., 2012, Volume 53, Number 4, Pages 781–793 (Mi smj2363)  

This article is cited in 8 scientific papers (total in 8 papers)

On complexity of three-dimensional hyperbolic manifolds with geodesic boundary

A. Yu. Vesninab, E. A. Fominykhcd

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Omsk State Technical University, Omsk
c Chelyabinsk State University, Chelyabinsk
d Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: The nonintersecting classes $\mathscr H_{p,q}$ are defined, with $p,q\in\mathbb N$ and $p\ge q\ge1$, of orientable hyperbolic $3$-manifolds with geodesic boundary. If $M\in\mathscr H_{p,q}$, then the complexity $c(M)$ and the Euler characteristic $\chi(M)$ of $M$ are related by the formula $c(M)=p-\chi(M)$. The classes $\mathscr H_{q,q}$, $q\ge1$, and $\mathscr H_{2,1}$ are known to contain infinite series of manifolds for each of which the exact values of complexity were found. There is given an infinite series of manifolds from $\mathscr H_{3,1}$ and obtained exact values of complexity for these manifolds. The method of proof is based on calculating the $\varepsilon$-invariants of manifolds.

Keywords: complexity of manifolds, hyperbolic manifolds.

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English version:
Siberian Mathematical Journal, 2012, 53:4, 625–634

Bibliographic databases:

UDC: 515.162
Received: 04.05.2012

Citation: A. Yu. Vesnin, E. A. Fominykh, “On complexity of three-dimensional hyperbolic manifolds with geodesic boundary”, Sibirsk. Mat. Zh., 53:4 (2012), 781–793; Siberian Math. J., 53:4 (2012), 625–634

Citation in format AMSBIB
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\paper On complexity of three-dimensional hyperbolic manifolds with geodesic boundary
\jour Sibirsk. Mat. Zh.
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\vol 53
\issue 4
\pages 781--793
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\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 4
\pages 625--634
\crossref{https://doi.org/10.1134/S0037446612040052}
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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. A. Yu. Vesnin, V. V. Tarkaev, E. A. Fominykh, “Three-dimensional hyperbolic manifolds with cusps of complexity 10 having maximal volume”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 227–239  mathnet  crossref  mathscinet  isi  elib
    2. A. Yu. Vesnin, E. A. Fominykh, “Two-sided bounds for the complexity of hyperbolic three-manifolds with geodesic boundary”, Proc. Steklov Inst. Math., 286 (2014), 55–64  mathnet  crossref  crossref  isi  elib  elib
    3. V. V. Tarkaev, E. A. Fominykh, “Verkhnie otsenki slozhnosti dopolnitelnykh prostranstv nekotorykh kruzhevnykh uzlov”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 6:3 (2014), 50–52  mathnet
    4. A. Yu. Vesnin, V. V. Tarkaev, E. A. Fominykh, “On the complexity of three-dimensional cusped hyperbolic manifolds”, Dokl. Math., 89:3 (2014), 267–270  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    5. A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Three-dimensional manifolds with poor spines”, Proc. Steklov Inst. Math., 288 (2015), 29–38  mathnet  crossref  crossref  isi  elib
    6. A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Complexity of virtual 3-manifolds”, Sb. Math., 207:11 (2016), 1493–1511  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. M. Ishikawa, K. Nemoto, “Construction of spines of two-bridge link complements and upper bounds of their Matveev complexities”, Hiroshima Math. J., 46:2 (2016), 149–162  mathscinet  zmath  isi
    8. 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  adsnasa  isi  elib
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