Multiplicities of simple closed geodesics and hypersurfaces in Teichm\"uller space
Geometric Topology
2014-11-11 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0701835,
title = {Multiplicities of simple closed geodesics and hypersurfaces in Teichm\"uller space},
author = {Greg McShane and Hugo Parlier},
journal= {arXiv preprint arXiv:math/0701835},
year = {2014}
}