Hyperbolic structures from Sol on pseudo-Anosov mapping tori

Abstract

The invariant measured foliations of a pseudo-Anosov homeomorphism induce a natural (singular) Sol structure on mapping tori of surfaces with pseudo-Anosov monodromy. We show that when the pseudo-Anosov $\varphi :S\to S$ has orientable foliations and does not have 1 as an eigenvalue of the induced cohomology action on the closed surface, then the Sol structure can be deformed to nearby cone hyperbolic structures, in the sense of projective structures. The cone angles can be chosen to be decreasing from multiples of $2\pi$.

various typos fixed, proof of smoothness rewritten to use Fox derivative, proof of Theorem 4.4 corrected, 29 pages, 3 figures

References in corpus (1)

• A Geometric transition from hyperbolic to anti de Sitter geometry

Cited by in corpus (4)

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• Extensions of Veech groups I: A hyperbolic action
• Character varieties of a transitioning Coxeter 4-orbifold
• Deformations of reducible SL(n,C) representations of fibered 3-manifold groups