Communications in Analysis and Geometry

Volume 31 (2023)

Number 4

Systole inequalities up congruence towers for arithmetic locally symmetric spaces

Pages: 847 – 878

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n4.a3

Authors

Sara Lapan (Department of Mathematics, University of California, Riverside, CA, USA)

Benjamin Linowitz (Department of Mathematics, Oberlin College, Oberlin, OH, USA)

Jeffrey S. Meyer (Department of Mathematics, California State University, San Bernardino, CA, USA)

Abstract

In this paper we study the systole growth of arithmetic locally symmetric spaces up congruence covers and show that this growth is at least logarithmic in volume. This generalizes previous work of Buser and Sarnak, and Katz, Schaps and Vishne in the context of compact arithmetic hyperbolic manifolds of dimension $2$ and $3$.

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Received 8 June 2020

Accepted 3 February 2021

Published 16 July 2024