Mathematics – Geometric Topology
Scientific paper
2007-01-29
Mathematics
Geometric Topology
Scientific paper
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.
McShane Greg
Parlier Hugo
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