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arxiv: 2405.12067 · v2 · submitted 2024-05-20 · 🧮 math.GT · math.GR

Atoroidal surface bundles

Autumn E. Kent , Christopher J. Leininger This is my paper
classification 🧮 math.GT math.GR
keywords surfaceatoroidalbundlesclassgroupmappingsurfacesclasses
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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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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. On fixed points of pseudo-Anosov maps

    math.GT 2025-09 unverdicted novelty 6.0

    Authors supply an estimate for fixed points of pseudo-Anosov maps and prove that, under strong irreducibility, log of the count is coarsely the Teichmuller length, plus volume-homology inequalities for mapping tori.