Hyperbolic Heegaard splittings and Dehn twists

Peter Feller; Alessandro Sisto; Gabriele Viaggi

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arXiv · 2304.05990

Hyperbolic Heegaard splittings and Dehn twists

Peter Feller·Alessandro Sisto·Gabriele Viaggi

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Abstract

We consider the family of Heegaard splittings of genus $g$ at least two which are defined via a gluing map that is the $n$-th power of the Dehn twist along a curve that satisfies a natural topological assumption, namely pared acylindricity. We show that if $n$ is at least 14, then the Heegaard splitting has a hyperbolic metric for which the simple closed curve defining the Dehn twist is a closed geodesic of length at least $1.24/(n^2g)$ and at most $37.5/n^2$

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Peter Feller, Alessandro Sisto, Gabriele Viaggi. 2023-04-12. Hyperbolic Heegaard splittings and Dehn twists. https://arxiv.org/abs/2304.05990

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