Non-arithmetic hybrid lattices in $\mathrm{PU}(2,1)$

TL;DR

This paper investigates hybrid subgroups within non-arithmetic lattices in PU(2,1), revealing that all of Mostow's lattices are virtually hybrids and some are formed from non-commensurable arithmetic lattices.

Contribution

It demonstrates that all Mostow's lattices are virtually hybrids and identifies certain non-arithmetic lattices as hybrids of non-commensurable arithmetic lattices.

Findings

All Mostow's lattices are virtually hybrids.

Some non-arithmetic lattices are hybrids of non-commensurable arithmetic lattices.

Hybrid structures exist within non-arithmetic lattices in PU(2,1).

Abstract

We explore hybrid subgroups of certain non-arithmetic lattices in $\mathrm{PU}(2,1)$. We show that all of Mostow's lattices are virtually hybrids; moreover, we show that some of these non-arithmetic lattices are hybrids of two non-commensurable arithmetic lattices in $\mathrm{PU}(1,1)$.