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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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Cite

BibTeXRIS
BibTeX
@misc{amrutam2026boundary,
  title = {{Boundary Dynamics, Cubical Actions, and Infinite Girth}},
  author = {Tattwamasi Amrutam and Arka Banerjee and Daniel L. Gulbrandsen and Pratyush Mishra},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.31124},
  eprint = {2608.31124},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.31124},
}
RIS
TY  - UNPB
TI  - Boundary Dynamics, Cubical Actions, and Infinite Girth
AU  - Tattwamasi Amrutam
AU  - Arka Banerjee
AU  - Daniel L. Gulbrandsen
AU  - Pratyush Mishra
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.31124
UR  - https://arxiv.org/abs/2608.31124
AB  - 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.
ER  -