On the number and location of short geodesics in moduli space

Christopher J. Leininger; Dan Margalit

doi:10.1112/jtopol/jts025

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arXiv · 1110.6434

On the number and location of short geodesics in moduli space

Christopher J. Leininger·Dan Margalit

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Abstract

A closed Teichmuller geodesic in the moduli space M_g of Riemann surfaces of genus g is called L-short if it has length at most L/g. We show that, for any L > 0, there exist e_2 > e_1 > 0, independent of g, so that the L-short geodesics in M_g all lie in the intersection of the e_1-thick part and the e_2-thin part. We also estimate the number of L-short geodesics in M_g, bounding this from above and below by polynomials in g whose degrees depend on L and tend to infinity as L does.

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BibTeX RIS

Christopher J. Leininger, Dan Margalit. 2011-10-28. On the number and location of short geodesics in moduli space. https://doi.org/10.1112/jtopol%2Fjts025

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