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On complexity of three-dimensional hyperbolic manifolds with geodesic boundary

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Abstract

The nonintersecting classes ℋ p,q are defined, with p, q ∈ ℕ and p ≥ q ≥ 1, of orientable hyperbolic 3-manifolds with geodesic boundary. If M ∈ ℋ p,q , then the complexity c(M) and the Euler characteristic χ(M) of M are related by the formula c(M) = p−χ(M). The classes ℋ q,q , q ≥ 1, and ℋ2,1 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 ℋ3,1 and obtained exact values of complexity for these manifolds. The method of proof is based on calculating the ɛ-invariants of manifolds.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. Yu. Vesnin

  2. Omsk State Technical University, Omsk, Russia

    A. Yu. Vesnin

  3. Chelyabinsk State University, Chelyabinsk, Russia

    E. A. Fominykh

  4. Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    E. A. Fominykh

Authors
  1. A. Yu. Vesnin
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  2. E. A. Fominykh
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Correspondence to A. Yu. Vesnin.

Additional information

Original Russian Text Copyright © 2012 Vesnin A.Yu. and Fominykh E.A.

The authors were supported by the Russian Foundation for Basic Research (Grants 10-01-00642 (Vesnin) and 11-01-00605 (Fominykh)) and the Leading Scientific Schools of the Russian Federation (Grants NSh-921.2012.1 (Vesnin) and NSh-1414.2012.1 (Fominykh)).

To the centenary of the birth of Academician Aleksandr Danilovich Alexandrov.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 4, pp. 781–793, July–August, 2012.

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Vesnin, A.Y., Fominykh, E.A. On complexity of three-dimensional hyperbolic manifolds with geodesic boundary. Sib Math J 53, 625–634 (2012). https://doi.org/10.1134/S0037446612040052

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  • DOI: https://doi.org/10.1134/S0037446612040052

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