Random group cobordisms of rank 7/4

TL;DR

This paper introduces a model for random groups of rank 7/4 and demonstrates that these groups exhibit the exponential mesoscopic rank property, contributing to the understanding of geometric properties in random group theory.

Contribution

It is the first to construct a random group model of rank 7/4 and analyze its exponential mesoscopic rank property.

Findings

Random groups of rank 7/4 can be modeled effectively.

These groups possess the exponential mesoscopic rank property.

The results advance understanding of geometric properties in random groups.

Abstract

We construct a model of random groups of rank 7/4, and show that in this model the random group has the exponential mesoscopic rank property.