The Klein bottle has stably unbounded homeomorphism group
Group Theory
2025-08-06 v2 Geometric Topology
Abstract
Using a recent result of Bowden, Hensel and Webb, we prove the existence of a homeomorphism with positive stable commutator length in the group of homeomorphisms of the Klein bottle which are isotopic to the identity.
Cite
@article{arxiv.2409.16772,
title = {The Klein bottle has stably unbounded homeomorphism group},
author = {Lukas Böke},
journal= {arXiv preprint arXiv:2409.16772},
year = {2025}
}
Comments
9 pages, 1 figure. Improved exposition, updated to reflect changes in main reference. Accepted by Glasgow Mathematical Journal