A C2-tilde-lattice that is not residually finite

TL;DR

This paper constructs the first example of a lattice on an irreducible Euclidean building that is not residually finite, challenging previous assumptions and suggesting potential extensions of the normal subgroup theorem.

Contribution

It provides the first known non-residually finite lattice on an irreducible Euclidean building, opening new directions in geometric group theory.

Findings

First example of a non-residually finite lattice on an irreducible Euclidean building

Supports conjecture that the normal subgroup theorem extends to this lattice

Indicates the potential for the lattice to be virtually simple

Abstract

We construct the first example of a lattice on an irreducible Euclidean building that is not residually finite. Conjecturally, the normal subgroup theorem extends to this lattice making it virtually simple.