Metric Geometry of Mapping Class and Relatively Hyperbolic Groups

Metric Geometry of Mapping Class and Relatively Hyperbolic Groups

Mon, 22/04
15:45 		David Hume (Oxford) Topology Seminar Add to calendar L3
Metric Geometry of Mapping Class and Relatively Hyperbolic Groups
We prove that quasi-trees of spaces satisfying the axiomatisation given by Bestvina, Bromberg and Fujiwara are quasi-isometric to tree-graded spaces in the sense of Dru\c{t}u and Sapir. We then present a technique for obtaining `good' embeddings of such spaces into $ \ell^p $ spaces, and show how results of Bestvina-Bromberg-Fujiwara and Mackay-Sisto allow us to better understand the metric geometry of such groups.