PreprintCC BY 4.0arXiv
Hyperbolicity and obstructions to PL actions of the circle
Abstract
We prove the following ``Torus Trichotomy Theorem'': every finitely generated subgroup of pls is either virtually free, a central extension of a cocompact Fuchsian group by a finite cyclic group, or a one-ended, non-acylindrically-hyperbolic group containing ℤ2. In particular, we obtain the ``free or surface'' alternative for word-hyperbolic groups of PL homeomorphisms of the circle.
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BibTeX
@misc{dinamarca2026hyperbolicity,
title = {{Hyperbolicity and obstructions to PL actions of the circle}},
author = {Leonardo Dinamarca and Maximiliano Escayola and Sang-hyun Kim and Thomas Koberda},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.12168},
eprint = {2608.12168},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.12168},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hyperbolicity and obstructions to PL actions of the circle
AU - Leonardo Dinamarca
AU - Maximiliano Escayola
AU - Sang-hyun Kim
AU - Thomas Koberda
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2608.12168
UR - https://arxiv.org/abs/2608.12168
AB - We prove the following ``Torus Trichotomy Theorem'': every finitely generated subgroup of pls is either virtually free, a central extension of a cocompact Fuchsian group by a finite cyclic group, or a one-ended, non-acylindrically-hyperbolic group containing ℤ^2. In particular, we obtain the ``free or surface'' alternative for word-hyperbolic groups of PL homeomorphisms of the circle.
ER -