Local maxima of the systole function

Fortier Bourque, M. and Rafi, K. (2022) Local maxima of the systole function. Journal of the European Mathematical Society, 24(2), pp. 623-668. (doi: 10.4171/JEMS/1113)

Abstract

We construct a sequence of closed hyperbolic surfaces that are local maxima for the systole function in their respective moduli spaces. Their systole is arbitrarily large and the number of examples grows rapidly with the genus. More precisely, for every n ≥ 3 there is some positive number Ln (growing roughly linearly in n) such that the number of local maxima of the systole function in genus g with systole equal to Ln grows super-exponentially in g along an arithmetic sequence of step size n. Many of these surfaces have no orientation-preserving isometries other than the identity and are the first examples of local maxima with this property.

• Item Type: Articles
• Additional Information: MFB and KR were partially supported by Discovery Grants from the Natural Sciences and Engineering Research Council of Canada (RGPIN 06768 and 06486 respectively).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Fortier-Bourque, Dr Maxime
• Authors: Fortier Bourque, M., and Rafi, K.
• College/School: College of Science and Engineering > School of Mathematics and Statistics
• Journal Name: Journal of the European Mathematical Society
• Publisher: European Mathematical Society
• ISSN: 1435-9855
• ISSN (Online): 1435-9863
• Published Online: 20 July 2021
• Copyright Holders: Copyright © 2021 EMS Publishing House
• First Published: First published in Journal of the European Mathematical Society 24(2): 623-668
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

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