Geodesic
The shape of the filling-systole subspace in surface moduli space and critical points of the systole function
Gao, Yue1
1 School of Mathematics and Statistics, Anhui Normal University, Wuhu, China
Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 2011-2038

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We study the space Xg ⊂ℳg consisting of surfaces with filling systoles and its subset, critical points of the systole function. In the first part we obtain a surface with Teichmüller distance 1 5 log ⁡ log ⁡ g to Xg, and in the second and third parts prove that most points in ℳg have Teichmüller distance 1 5 log ⁡ log ⁡ g and Weil–Petersson distance 0.6521(log ⁡ g −7 log ⁡ log ⁡ g) to Xg. So the radius-r neighborhood of Xg cannot cover the thick part of ℳg for any fixed r > 0. In the last two parts, we get critical points with small and large (comparable to the diameter of the thick part of ℳg) distances.

DOI : 10.2140/agt.2024.24.2011
Keywords: filling systole subspace, sparseness, random surfaces, Weil–Petersson metric, critical points of the systole function

Gao, Yue 1

1 School of Mathematics and Statistics, Anhui Normal University, Wuhu, China 
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Gao, Yue. The shape of the filling-systole subspace in surface moduli space and critical points of the systole function. Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 2011-2038. doi: 10.2140/agt.2024.24.2011

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