Profinite isomorphisms, stable commutator length, and fixed point properties
Group Theory
2026-03-13 v1 Geometric Topology
Abstract
We construct Grothendieck pairs witnessing that the following are not profinite invariants: stable commutator length, quasimorphisms (answering a question of Echtler and Kammeyer), property NL (which obstructs actions on hyperbolic spaces), and property FW (which obstructs actions on finite-dimensional CAT(0) cube complexes). We also recover that property FA and non-abelian free subgroups are not profinite invariants. The method combines Rips constructions with iterated group-theoretic Dehn filling on hyperbolic virtually special groups.
Cite
@article{arxiv.2603.12095,
title = {Profinite isomorphisms, stable commutator length, and fixed point properties},
author = {Francesco Fournier-Facio},
journal= {arXiv preprint arXiv:2603.12095},
year = {2026}
}
Comments
21 pages