Thin actions on CAT(0) spaces
Metric Geometry
2022-11-29 v3
Abstract
We study groups of isometries of packed, geodesically complete, CAT-spaces for which the systole at every point is smaller than a universal constant depending only on the packing, deducing strong rigidity results. We show that if a space as above has some negative curvature behaviour then it cannot support a thin action: this generalizes the classical Margulis Lemma to a broader class of spaces.
Cite
@article{arxiv.2210.01085,
title = {Thin actions on CAT(0) spaces},
author = {Nicola Cavallucci and Andrea Sambusetti},
journal= {arXiv preprint arXiv:2210.01085},
year = {2022}
}
Comments
v2: Correction of minor errors in Step 3 of the proof of Theorem 3.1. Remark 3.4 accordingly updated v3: Affiliations added