Rank Rigidity for CAT(0) spaces without 3-flats
Metric Geometry
2022-12-15 v1 Differential Geometry
Group Theory
Geometric Topology
Abstract
If a group acts geometrically on a CAT(0) space without 3-flats, then either contains a -periodic geodesic which does not bound a flat half-plane, or else is a rank 2 Riemannian symmetric space, a 2-dimensional Euclidean building or non-trivially splits as a metric product. Consequently all such groups satisfy a strong form of the Tits Alternative.
Keywords
Cite
@article{arxiv.2212.07100,
title = {Rank Rigidity for CAT(0) spaces without 3-flats},
author = {Stephan Stadler},
journal= {arXiv preprint arXiv:2212.07100},
year = {2022}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2202.02302