CAT(0) spaces with boundary the join of two Cantor sets
Metric Geometry
2014-10-01 v4 Group Theory
Geometric Topology
Abstract
We will show that if a proper complete CAT(0) space X has a visual boundary homeomorphic to the join of two Cantor sets, and X admits a geometric group action by a group containing a subgroup isomorphic to Z^2, then its Tits boundary is the spherical join of two uncountable discrete sets. If X is geodesically complete, then X is a product, and the group has a finite index subgroup isomorphic to a lattice in the product of two isometry groups of bounded valence bushy trees.
Cite
@article{arxiv.1204.1047,
title = {CAT(0) spaces with boundary the join of two Cantor sets},
author = {Khek Lun Harold Chao},
journal= {arXiv preprint arXiv:1204.1047},
year = {2014}
}
Comments
14 pages, 2 figures; v4: added a missing assumption in the main results