We exhibit closed hyperbolic manifolds with arbitrarily small systole in each
dimension that are not quasiarithmetic 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.
Keywords
geometry, topology, hyperbolic manifolds, systolic
geometry, discrete subgroups of Lie groups
