Abstract
We will show that if a proper complete space has a visual boundary homeomorphic to the join of two Cantor sets, and admits a geometric group action by a group containing a subgroup isomorphic to , then its Tits boundary is the spherical join of two uncountable discrete sets. If is geodesically complete, then 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.
Citation
Khek Lun Harold Chao. "$\mathrm{CAT}(0)$ spaces with boundary the join of two Cantor sets." Algebr. Geom. Topol. 14 (2) 1107 - 1122, 2014. https://doi.org/10.2140/agt.2014.14.1107
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