Fibered 3-manifolds and Veech groups

Nicholas Rouse, Kasra Rafi, Christopher Leininger, Emily Shinkle, Yvon Verberne

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.

Mathematics Subject Classification ID

2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20) Hyperbolic 3-manifolds (57K32)

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