English

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

Metric Geometry 2010-11-09 v2

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.

Cite

@article{arxiv.1010.1963,
  title  = {CAT(0) spaces on which a certain type of singularity is bounded},
  author = {Tetsu Toyoda},
  journal= {arXiv preprint arXiv:1010.1963},
  year   = {2010}
}

Comments

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

R2 v1 2026-06-21T16:26:25.491Z