Geodesic
CAT(0) spaces with boundary the join of two Cantor sets
Chao, Khek Lun Harold1
1Department of Mathematics, Indiana University, Bloomington, IN 47405, USA
Algebraic and Geometric Topology, Tome 14 (2014) no. 2, pp. 1107-1122
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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 ℤ2, 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.

DOI : 10.2140/agt.2014.14.1107
Classification : 20F65, 20F67, 51F99
Keywords: CAT(0) space, CAT(0) group, Cantor set, join, spherical join, Tits boundary, visual boundary

Chao, Khek Lun Harold  1

1 Department of Mathematics, Indiana University, Bloomington, IN 47405, USA 
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Chao, Khek Lun Harold. CAT(0) spaces with boundary the join of two Cantor sets. Algebraic and Geometric Topology, Tome 14 (2014) no. 2, pp. 1107-1122. doi: 10.2140/agt.2014.14.1107

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