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arXiv · 2608.31124

Boundary Dynamics, Cubical Actions, and Infinite Girth

Tattwamasi Amrutam·Arka Banerjee·Daniel L. Gulbrandsen·Pratyush Mishra
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Abstract

We develop two methods for proving infinite girth from boundary dynamics. First, we use topologically free extreme boundary actions to give a boundary-dynamical proof of infinite girth for finitely generated acylindrically hyperbolic groups. The second combines Nakamura's criterion with, respectively, flag-space and Roller-boundary dynamics, yielding infinite-girth results for semisimple $S$-algebraic groups and for essential non-elementary actions on finite-dimensional, second countable, non-Euclidean CAT(0) cube complexes. We also prove that every finitely generated large group has infinite girth, thereby answering a question of Akhmedov and Mishra.

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Tattwamasi Amrutam, Arka Banerjee, Daniel L. Gulbrandsen, Pratyush Mishra. 2026-08-31. Boundary Dynamics, Cubical Actions, and Infinite Girth. https://arxiv.org/abs/2608.31124

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