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2008 Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space
Greg McShane, Hugo Parlier
Geom. Topol. 12(4): 1883-1919 (2008). 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.

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Greg McShane. Hugo Parlier. "Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space." Geom. Topol. 12 (4) 1883 - 1919, 2008. https://doi.org/10.2140/gt.2008.12.1883

Information

Received: 25 July 2007; Revised: 1 May 2008; Accepted: 7 January 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1154.57016
MathSciNet: MR2431011
Digital Object Identifier: 10.2140/gt.2008.12.1883

Subjects:
Primary: 57M50
Secondary: 58D99

Rights: Copyright © 2008 Mathematical Sciences Publishers

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