This Thursday at U. Haifa Topology & Geometry seminar on March 7, 2019 at 12:10
Geometry & Topology Seminar
Speaker: Alex Margolis (Technion)
Topic: Quasi-isometric rigidity of groups containing almost normal
subgroups
Place: room 614 in the Science & Education Building
Time 12:10
Date: Thursday, March 7, 2019
Abstract:
A goal of geometric group theory is to understand to what extent the
large scale geometry of a finitely generated group determines its
algebraic structure. A subgroup H of G is said to be almost normal if
every conjugate of H is commensurable to H. If G is finitely generated
and H is almost normal, then G can be thought of as a coarse bundle
over the coset space G/H. We show that quasi-isometries frequently
preserve almost normal subgroups and the associated coarse bundle
structure. A sample application is the following: any finitely
presented group quasi-isometric to a Z-by-(∞ ended) group is also Z-by-
(∞ ended). We make use of the notion of relative ends due to Kropholler
and Roller. Our results build on work of Dunwoody and Mosher-Sageev-
Whyte.
