Elements with north-south dynamics and free subgroups have positive density in Thompson's groups T and V

TL;DR

This paper demonstrates that elements with north-south dynamics and pairs generating free subgroups are positively dense in Thompson's groups T and V, indicating rich subgroup structures.

Contribution

It establishes positive density results for elements with specific dynamics and free subgroups in Thompson's groups T and V, revealing their complex subgroup spectra.

Findings

Positive density of elements with north-south dynamics in T and V

Positive density of element pairs generating free subgroups in T and V

Thompson's groups contain rich free subgroup structures

Abstract

We show that the density of elements in Thompson's groups T and V which have north-south dynamics acting on the circle is positive with respect to a stratification in terms of size. We show that the fraction of element pairs which generate a free subgroup of rank two is positive in both groups with respect to a stratification based on diagram size, which shows that the associated subgroup spectra of $T$ and $V$ contain free groups.