Braids, entropies and fibered 2-fold branched covers of 3-manifolds

Susumu Hirose; Eiko Kin

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arXiv · 2210.00661

Braids, entropies and fibered 2-fold branched covers of 3-manifolds

Susumu Hirose·Eiko Kin

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Abstract

It is proved by Sakuma and Brooks that any closed orientable $3$-manifold with a Heegaard splitting of genus $g$ admits a $2$-fold branched cover that is a hyperbolic $3$-manifold and a genus $g$ surface bundle over the circle. This paper concerns entropy of pseudo-Anosov monodromies for hyperbolic fibered $3$-manifolds. We prove that there exist infinitely many closed orientable $3$-manifolds $M$ such that the minimal entropy over all hyperbolic, genus $g$ surface bundles over the circle as $2$-fold branched covers of the $3$-manifold $M$ is comparable to $1/g$.

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Susumu Hirose, Eiko Kin. 2022-10-03. Braids, entropies and fibered 2-fold branched covers of 3-manifolds. https://arxiv.org/abs/2210.00661

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