The maximal systole of hyperbolic surfaces with maximal $S^3$-extendable abelian symmetry

Yue Gao and Jiajun Wang

Vol. 325 (2023), No. 1, 85–104

DOI: 10.2140/pjm.2023.325.85

Abstract

We study the maximal systole of hyperbolic surfaces with certain symmetries. We give the formula for the maximal systole of the surfaces that admit the largest $S^3$-extendable abelian group symmetry. The result is obtained by parametrizing such surfaces and enumerating all possible systoles.

Keywords

systole, hyperbolic surfaces, $S^3$-extendable symmetry

Mathematical Subject Classification

Primary: 30F45

Milestones

Received: 28 November 2021

Revised: 18 June 2023

Accepted: 21 June 2023

Published: 3 September 2023