On the number and location of short geodesics in moduli space

Details On the number and location of short geodesics in moduli space On the number and location of short geodesics in moduli space

2011-10-28

arxiv.org/abs/1110.6434v1

Mathematics

Geometric Topology

23 pages, 1 figure

Scientific paper

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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