In this paper we prove that, for any arithmetic hyperbolic -manifold of the first type, the systole of most of the principal congruence coverings satisfy
where is a constant independent of . This generalizes previous work of Buser and Sarnak, and Katz, Schaps, and Vishne in dimension 2 and 3. As applications, we obtain explicit estimates for systolic genus of hyperbolic manifolds studied by Belolipetsky and the distance of homological codes constructed by Guth and Lubotzky. In Appendix A together with Cayo Dória we prove that the constant is sharp.
Cite this article
Plinio G.P. Murillo, Systole of congruence coverings of arithmetic hyperbolic manifolds. Groups Geom. Dyn. 13 (2019), no. 3, pp. 1083–1102DOI 10.4171/GGD/515