Atoroidal surface bundles

Autumn E. Kent; Christopher J. Leininger

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arXiv · 2405.12067

Atoroidal surface bundles

Autumn E. Kent·Christopher J. Leininger

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Abstract

We show that there is a type-preserving homomorphism from the fundamental group of the figure-eight knot complement to the mapping class group of the thrice-punctured torus. As a corollary, we obtain infinitely many commensurability classes of purely pseudo-Anosov surface subgroups of mapping class groups of closed surfaces. This gives the first examples of compact atoroidal surface bundles over surfaces.

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Autumn E. Kent, Christopher J. Leininger. 2024-05-20. Atoroidal surface bundles. https://arxiv.org/abs/2405.12067

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