CAT(0) spaces with boundary the join of two Cantor sets
arXiv:1204.1047 · doi:10.2140/agt.2014.14.1107
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.
14 pages, 2 figures; v4: added a missing assumption in the main results