Systole on locally symmetric spaces

Abstract

Here we survey the systole growth of arithmetic locally symmetric spaces under congruence covering and give a simple proof for the best possible Gromov constant for several important classes of symmetric spaces. Contents

On the systole growth in congruence quaternionic hyperbolic manifolds

“…However, the values of the constants obtained in [10] are not optimal, as the comparison with the results mentioned above shows. See also [9]. This paper is dedicated to improving the constant for quaternionic hyperbolic spaces.…”