Volume 20, issue 1 (2016)

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Hyperbolic structures from Sol on pseudo-Anosov mapping tori

Kenji Kozai

Geometry & Topology 20 (2016) 437–468

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 ϕ: S 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 2π.

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Sol, fibered $3$–manifold, projective structure, regeneration
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 57R20, 55N25
Received: 22 July 2014
Revised: 19 April 2015
Accepted: 21 May 2015
Published: 29 February 2016
Proposed: Ian Agol
Seconded: Jean-Pierre Otal, David Gabai
Kenji Kozai
Department of Mathematics
University of California, Berkeley
970 Evans Hall #3840
Berkeley, CA 94720-3840