Random groups contain surface subgroups

TL;DR

This paper demonstrates that random groups, in a probabilistic sense, almost surely contain numerous quasiconvex surface subgroups, highlighting rich geometric subgroup structures within these groups.

Contribution

It establishes that random groups generically contain surface subgroups, advancing understanding of their geometric and subgroup properties.

Findings

Random groups contain many quasiconvex surface subgroups

Surface subgroups are prevalent in generic random groups

The result applies broadly to various models of random groups

Abstract

A random group contains many quasiconvex surface subgroups.