CAT(0) spaces on which a certain type of singularity is bounded

Details CAT(0) spaces on which a certain type of singularity is bounded CAT(0) spaces on which a certain type of singularity is bounded

2010-10-10

arxiv.org/abs/1010.1963v2

Mathematics

Metric Geometry

To appear in Kodai Math. J. 33 (2010)

Scientific paper

In this paper, we present a geometric condition for a family of CAT(0) spaces, which ensures that the Izeki-Nayatani invariants of spaces in the family are uniformly bounded from above by a constant strictly less than 1. Each element of such a family with this condition is a space presented by M. Gromov as an example of a "CAT(0) space with "bounded" singularities". Combining our result with a result of Izeki, Kondo and Nayatani, we see that random groups of Gromov's graph model have a fixed-point property for such a family.

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