Minimal displacement set for weakly systolic complexes
Group Theory
2024-09-09 v1 Combinatorics
Geometric Topology
Metric Geometry
Abstract
We investigate the structure of the minimal displacement set in weakly systolic complexes. We show that such set is systolic and that it embeds isometrically into the complex. As corollaries, we prove that any isometry of a weakly systolic complex either fixes the barycentre of some simplex (elliptic case) or it stabilizes a thick geodesic (hyperbolic case).
Keywords
Cite
@article{arxiv.2409.03850,
title = {Minimal displacement set for weakly systolic complexes},
author = {Ioana-Claudia Lazar},
journal= {arXiv preprint arXiv:2409.03850},
year = {2024}
}
Comments
11 pages, 4 figures