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Behavior of the extended complexity of irreducible 3-manifolds

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Abstract

We construct the extended complexity of irreducible 3-manifolds; unlike the usual complexity [1] it is not an integer, but an ordered tuple of five integers. The benefit of extended complexity is that it always decreases when a manifold is cut along some incompressible boundary incompressible surface.

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References

  1. Matveev S. V., Algorithmic Topology and Classification of 3-Manifolds [in Russian], MTsNMO, Moscow (2007).

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  2. Shatnykh O., “The extended complexity of 3-manifolds,” Siberian Electronic Math. Reports, V. 2, 194–195 (2005).

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Authors and Affiliations

  1. Kurgan State University, Kurgan, Russia

    O. N. Shatnykh

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  1. O. N. Shatnykh
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Correspondence to O. N. Shatnykh.

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Original Russian Text Copyright © 2008 Shatnykh O. N.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 3, pp. 698–706, May–June, 2008.

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Shatnykh, O.N. Behavior of the extended complexity of irreducible 3-manifolds. Sib Math J 49, 562–568 (2008). https://doi.org/10.1007/s11202-008-0053-5

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  • DOI: https://doi.org/10.1007/s11202-008-0053-5

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