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

Sean Cleary; Ariadna Fossas Tenas

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arXiv · 2006.03115

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

Sean Cleary·Ariadna Fossas Tenas

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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.

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Sean Cleary, Ariadna Fossas Tenas. 2020-06-04. Elements with north-south dynamics and free subgroups have positive density in Thompson's groups T and V. https://arxiv.org/abs/2006.03115

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