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arXiv · 1010.1963

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

Tetsu Toyoda
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Abstract

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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Tetsu Toyoda. 2010-10-10. CAT(0) spaces on which a certain type of singularity is bounded. https://arxiv.org/abs/1010.1963

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