Hyperbolic structures from Sol on pseudo-Anosov mapping tori

Kozai, Kenji

doi:10.2140/gt.2016.20.437

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Hyperbolic structures from Sol on pseudo-Anosov mapping tori

Kenji Kozai

Geometry & Topology 20 (2016) 437–468

DOI: 10.2140/gt.2016.20.437

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 $ϕ : S \to S$ 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 $2 π$ .

Keywords

Sol, fibered $3$–manifold, projective structure, regeneration

Mathematical Subject Classification 2010

Primary: 57M50

Secondary: 57R20, 55N25

References

Publication

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

Authors

Kenji Kozai
Department of Mathematics University of California, Berkeley 970 Evans Hall #3840 Berkeley, CA 94720-3840 USA
http://math.berkeley.edu/~kozai/

Volume 20, issue 1 (2016)