Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space

McShane, Greg; Parlier, Hugo

doi:10.2140/gt.2008.12.1883

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

Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space

Greg McShane and Hugo Parlier

Geometry & Topology 12 (2008) 1883–1919

DOI: 10.2140/gt.2008.12.1883

Abstract

Using geodesic length functions, we define a natural family of real codimension 1 subvarieties of Teichmüller space, namely the subsets where the lengths of two distinct simple closed geodesics are of equal length. We investigate the point set topology of the union of all such hypersurfaces using elementary methods. Finally, this analysis is applied to investigate the nature of the Markoff conjecture.

Keywords

simple closed geodesic, Teichmüller spaces, hyperbolic surface

Mathematical Subject Classification 2000

Primary: 57M50

Secondary: 58D99

References

Publication

Received: 25 July 2007

Revised: 1 May 2008

Accepted: 7 January 2008

Published: 5 July 2008

Proposed: Benson Farb

Seconded: Dave Gabai, Jean-Pierre Otal

Authors

Greg McShane
Laboratoire Emile Picard Université Paul Sabatier Toulouse France

Hugo Parlier
Section de Mathématiques École Polytechnique Fédérale de Lausanne SB-IGAT-CTG, BCH CH-1015 Lausanne Switzerland

Volume 12, issue 4 (2008)