Affiliation:
1. DMA, École normale supérieure Université PSL, CNRS Paris France
2. Instytut Matematyczny Uniwersytet Wrocławski Wrocław Poland
3. Department of Mathematics Cornell University Ithaca New York USA
Abstract
AbstractWe prove that asymptotic cones of Helly graphs are countably hyperconvex. We use this to show that virtually nilpotent Helly groups are virtually abelian and to characterize virtually abelian Helly groups via their point groups. In fact, we do this for the more general class of coarsely injective spaces and groups. We apply this to prove that the 3‐3‐3‐Coxeter group is not Helly (nor even coarsely injective), thus obtaining the first example of a systolic group that is not Helly, answering a question of Chalopin, Chepoi, Genevois, Hirai, and Osajda.
Funder
European Research Council
Narodowe Centrum Nauki
Natural Sciences and Engineering Research Council of Canada
Simons Foundation