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

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

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
\Bibitem{VesFom12} \by A.~Yu.~Vesnin, E.~A.~Fominykh \paper On complexity of three-dimensional hyperbolic manifolds with geodesic boundary \jour Sibirsk. Mat. Zh. \yr 2012 \vol 53 \issue 4 \pages 781--793 \mathnet{http://mi.mathnet.ru/smj2363} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3013526} \transl \jour Siberian Math. J. \yr 2012 \vol 53 \issue 4 \pages 625--634 \crossref{https://doi.org/10.1134/S0037446612040052} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000307983400005} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865462828} 

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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
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
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
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
5. A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Three-dimensional manifolds with poor spines”, Proc. Steklov Inst. Math., 288 (2015), 29–38
6. A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Complexity of virtual 3-manifolds”, Sb. Math., 207:11 (2016), 1493–1511
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
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
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