Hyperbolic surfaces with sublinearly many systoles that fill

Fortier Bourque, M. (2020) Hyperbolic surfaces with sublinearly many systoles that fill. Commentarii Mathematici Helvetici, 95(3), pp. 515-534. (doi: 10.4171/CMH/495)

Abstract

For any ε>0, we construct a closed hyperbolic surface of genus g=g(ε) with a set of at most εg systoles that fill, meaning that each component of the complement of their union is contractible. This surface is also a critical point of index at most εg for the systole function, disproving the lower bound of 2g−1 conjectured by Schmutz Schaller.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Fortier-Bourque, Dr Maxime
• Authors: Fortier Bourque, M.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Commentarii Mathematici Helvetici
• Publisher: European Mathematical Society
• ISSN: 0010-2571
• ISSN (Online): 1420-8946
• Copyright Holders: Copyright © 2019 The Author
• First Published: First published in Commentarii Mathematici Helvetici 95(3):515-534
• Publisher Policy: Reproduced in accordance with the publisher copyright policy