Multiplicities of simple closed geodesics and hypersurfaces in Teichmuller space

Using geodesic length functions, we define a natural family of real codimension 1 subvarieties of Teichmuller 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.


Published in:
Geometry & Topology, 12, 1883-1919
Year:
2008
Keywords:
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 Record created 2010-11-30, last modified 2018-01-28


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