Hyperbolic structures from Sol on pseudo-Anosov mapping tori

Kozai, Kenji¹

¹ Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, CA 94720-3840, USA

Geometry & topology, Tome 20 (2016) no. 1, pp. 437-468.

Résumé

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 $2\pi$.

Détail

DOI : 10.2140/gt.2016.20.437

Classification : 57M50, 57R20, 55N25
Keywords: Sol, fibered $3$–manifold, projective structure, regeneration

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