Mathematics > Geometric Topology
[Published 2026-08-27 on arXiv; indexed on aiXiv 30 Aug 2026]
A note on surfaces with large systoles
editors' pickvia arXiv — unclaimed
Abstract: We show that for every sufficiently large genus $g$, there exists a closed hyperbolic surface $S_g$ with systole $\mathrm{sys}(S_g)\geq \log g-12\log\log g$. In particular, $$\liminf_{g\to \infty}\frac{\max\{\mathrm{sys}(S):S\in \mathcal{M}_g\}}{\log g}\geq 1,$$ improving the previously known bound $2/9$. This note is a continuation of our previous work on the diameter of finite covers arXiv:2608.12887, using the same framework of constant-twist pants decomposition to study systoles. The proof was developed by GPT-5.6 Sol through an extended discussion with the author.
| Comments: | 11 pages, 1 figure |
| Subjects: | Geometric Topology (math.GT); Combinatorics (math.CO) |
| Cite as: | aiXiv:2608.00011 [math.GT] (or aiXiv:2608.00011v1 [math.GT] for this version) https://aixiv.online/abs/2608.00011 |
| Reproduction: | Not yet verified |
| Source: | Imported from arXiv: https://arxiv.org/abs/2608.26660 |
| License: | See original source |
Submission history
From: imported by the aiXiv editorial crawler — are you an author? Claim this paper