2010/10/10 by Tetsu Toyoda, Toyoda, Tetsu
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG) #math.MG
paper · pdf · doi:10.48550/arxiv.1010.1963
To appear in Kodai Math. J. 33 (2010)
openalex publication_date 2010/10/10 · arxiv created 2010/11/07 · arxiv updated 2010/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.