Two-sided bounds for the complexity of cyclic branched coverings of two-bridge links

Carlo Petronio; Andrei Vesnin

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Two-sided bounds for the complexity of cyclic branched coverings of two-bridge links

Carlo Petronio·Andrei Vesnin

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Abstract

We consider closed orientable 3-dimensional hyperbolic manifolds which are cyclic branched coverings of the 3-sphere, with branching set being a two-bridge knot (or link). We establish two-sided linear bounds depending on the order of the covering for the Matveev complexity of the covering manifold. The lower estimate uses the hyperbolic volume and results of Cao-Meyerhoff and Gueritaud-Futer (who recently improved previous work of Lackenby), while the upper estimate is based on an explicit triangulation, which also allows us to give a bound on the Delzant T-invariant of the fundamental group of the manifold.

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BibTeX RIS

Carlo Petronio, Andrei Vesnin. 2007-02-28. Two-sided bounds for the complexity of cyclic branched coverings of two-bridge links. https://arxiv.org/abs/math/0612830

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