Geometric Group Therapy Seminar

Speaker: Mateusz Kandybo

Title: CAT(0)-boundaries of graphs of groups are dense amalgams

Abstract: In 2016 Świątkowski examined non-elementary graphs of groups with finite edge groups and all vertex groups being CAT(0). He showed that the fundamental group of said graphs of groups admits a CAT(0)-boundary which is homeomorphic to a dense amalgam of CAT(0)-boundaries of vertex groups. In this talk we will also investigate the behavior of boundaries of such a fundamental groups and observe a result that is almost the converse of the aforementioned theorem. Namely, we will see that any CAT(0)-boundary of the discussed graph of groups is homeomorphic to a dense amalgam of limit sets of vertex groups. This result is an offshoot of the speaker’s bachelor thesis written under supervision of Jacek Świątkowski.