Effective hyperbolization and length bounds for Heegaard splittings

Peter Feller; Alessandro Sisto; Gabriele Viaggi

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arXiv · 2408.06998

Effective hyperbolization and length bounds for Heegaard splittings

Peter Feller·Alessandro Sisto·Gabriele Viaggi

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Abstract

We consider 3-manifolds given as Heegaard splittings $M=H^-\cup_\Sigma H^+$ with the aim to describe the hyperbolic metric of $M$ under topological conditions on the splitting guaranteeing that the manifold is hyperbolic. In particular, given a suitable "sufficiently incompressible" curve $\gamma\subset\Sigma$, we show (without appealing to Geometrization) that $M$ is hyperbolic and we compute the length of $\gamma$ in terms of the projection coefficients of the disk sets, up to a uniform multiplicative error.

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BibTeX RIS

Peter Feller, Alessandro Sisto, Gabriele Viaggi. 2024-08-13. Effective hyperbolization and length bounds for Heegaard splittings. https://arxiv.org/abs/2408.06998

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