Home >> Seminar 

Boundaries of nonpositively curved groups
Yulan Qing(University of Toronto)
Tuesday, July 23rd, 2019, 10:30 AM 中北校区田家炳楼110 

摘要:
To every Gromov hyperbolic space X one can associate a space at infinity called the Gromov boundary of X. This boundary is a fundamental tool for studying hyperbolic groups and hyperbolic 3manifolds. As shown by Gromov, quasiisometries of hyperbolic metric spaces induce homeomorphisms on their boundaries, thus giving rise to a welldefined notion of the boundary of a hyperbolic group. Croke and Kleiner showed that visual boundary of nonpositively curved (CAT(0)) groups is not welldefined, since quasiisometric CAT(0) spaces can have nonhomeomorphic boundaries. For any sublinear function, we consider a subset of the visual boundary called sublinear boundary and show that it is a QIinvariant. This is to say, the sublinearboundary of a CAT(0) group is welldefined. In the case of Rightangled Artin group, we show that the Poisson boundary of random walks on groups is naturally identified with the (log t)boundary. This talk is based on projects with Kasra Rafi and Giulio Tiozzo.
关键词：几何群论，测底线，边界，非正曲率空间，随机游走。
邀请人：杜若霞



