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)