Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space

Greg McShane, Hugo Parlier
2008 Geometry and Topology  
Using geodesic length functions, we define a natural family of real codimension 1 subvarieties of Teichm\"uller 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.
doi:10.2140/gt.2008.12.1883 fatcat:6anqno4fefgtnljb3pqtrfnkue