Random surfaces with large systoles
Geometric Topology
2024-03-04 v2 Combinatorics
Group Theory
Probability
Abstract
We present two constructions, both inspired by ideas from graph theory, of sequences random surfaces of growing area, whose systoles grow logarithmically as a function of their area. This also allows us to prove a new lower bound on the maximal systole of a closed orientable hyperbolic surface of a given genus.
Cite
@article{arxiv.2312.11428,
title = {Random surfaces with large systoles},
author = {Mingkun Liu and Bram Petri},
journal= {arXiv preprint arXiv:2312.11428},
year = {2024}
}
Comments
32 pages, 3 figures. A new result regarding the lower bound on the maximal systole of a closed hyperbolic surface of a given genus has been added