Mathematics – Geometric Topology
Scientific paper
2006-12-28
Osaka J. Math. 46 (2009), 1077-1095
Mathematics
Geometric Topology
Estimates improved using recent results of Gueritaud-Futer and Kim-Kim
Scientific paper
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.
Petronio Carlo
Vesnin Andrei
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