CAT(0) spaces with boundary the join of two Cantor sets

Details CAT(0) spaces with boundary the join of two Cantor sets CAT(0) spaces with boundary the join of two Cantor sets

2012-04-04

arxiv.org/abs/1204.1047v2

Mathematics

Metric Geometry

11 pages, 2 figures; v2: corrected statements of Theorems 1.2, 5.5 (was 5.4), changed a remark to Corollary 5.4

Scientific paper

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 isometries, then its Tits boundary is the spherical join of two
uncountable discrete sets. If X is geodesically complete, then X is reducible.

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