Systoles of hyperbolic hybrids

TL;DR

This paper constructs hyperbolic manifolds with arbitrarily small systoles that are not quasi-arithmetic, expanding the known examples beyond those previously constructed by other researchers.

Contribution

It introduces a new method of creating hyperbolic manifolds with small systoles that are not quasi-arithmetic, using hybridization of existing manifolds.

Findings

Existence of hyperbolic manifolds with arbitrarily small systoles

Construction of non-quasi-arithmetic hyperbolic manifolds

Extension beyond previously known examples

Abstract

We exhibit closed hyperbolic manifolds with arbitrarily small systole in each dimension that are not quasi-arithmetic in the sense of Vinberg, and are thus not commensurable to those constructed by Agol, Belolipetsky--Thomson, and Bergeron--Haglund--Wise. This is done by taking hybrids of the manifolds constructed by the latter authors.