Covers of surfaces, Kleinian groups, and the curve complex

Tarik Aougab; Priyam Patel; Samuel J. Taylor

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arXiv · 1810.12953

Covers of surfaces, Kleinian groups, and the curve complex

Tarik Aougab·Priyam Patel·Samuel J. Taylor

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Abstract

We prove an effective version of a theorem relating curve complex distance to electric distance in hyperbolic 3-manifolds, up to errors that are polynomial in the complexity of the underlying surface. We use this to give an effective proof of a result regarding maps between curve complexes of surfaces induced by finite covers. As applications, we effectively relate the electric circumference of a fibered manifold to the curve complex translation length of its monodromy, and we give quantitative bounds on virtual specialness for cube complexes dual to curves on surfaces.

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BibTeX RIS

Tarik Aougab, Priyam Patel, Samuel J. Taylor. 2018-10-30. Covers of surfaces, Kleinian groups, and the curve complex. https://arxiv.org/abs/1810.12953

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