香蕉视频

Title:聽Crystallographic Helly groups.

Abstract:聽A Helly graph is a graph in which the metric balls form a Helly family: any pairwise intersecting collection of balls has nonempty total intersection. A Helly group is a group that acts properly and cocompactly on a Helly graph. Helly groups simultaneously generalize hyperbolic, cocompactly cubulated and C(4)-T(4) graphical small cancellation groups while maintaining nice properties, such as biautomaticity. I will show that if a crystallographic group is Helly then its point group preserves an L^{infinity} metric on R^n. Thus we will obtain some new nonexamples of Helly groups, including the 3-3-3 Coxeter group, which is a systolic group. This answers a question posed by Chepoi during the recent Simons Semester on Geometric and Analytic Group Theory in Warsaw.