Fibered 3-manifolds and Veech groups

Christopher J. Leininger; Kasra Rafi; Nicholas Rouse; Emily Shinkle; Yvon Verberne

doi:10.2140/agt.2025.25.1897

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arXiv · 2212.13320

Fibered 3-manifolds and Veech groups

Christopher J. Leininger·Kasra Rafi·Nicholas Rouse·Emily Shinkle·Yvon Verberne

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Abstract

We study Veech groups associated to the pseudo-Anosov monodromies of fibers and foliations of a fixed hyperbolic 3-manifold. Assuming Lehmer's Conjecture, we prove that the Veech groups associated to fibers generically contain no parabolic elements. For foliations, we prove that the Veech groups are always elementary.

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Christopher J. Leininger, Kasra Rafi, Nicholas Rouse, Emily Shinkle, Yvon Verberne. 2022-12-26. Fibered 3-manifolds and Veech groups. https://doi.org/10.2140/agt.2025.25.1897

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