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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 4, Pages 781–793
(Mi smj2363)
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This article is cited in 10 scientific papers (total in 10 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.
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
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https://www.mathnet.ru/eng/smj2363 https://www.mathnet.ru/eng/smj/v53/i4/p781
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Abstract page: | 373 | Full-text PDF : | 97 | References: | 53 | First page: | 2 |
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