Date:
Thu, 27/03/202516:00-17:00
Location:
Ross 70
Groups and dynamics seminar
Time: Thursday, 27/4, 16:00 (Note the special time)
Place: Ross 70
Speaker: Zachary Munro (Technion)
Title: Richly branching flats and strict small-cancellation
Abstract:
I will discuss two projects addressing cubulability of small-cancellation groups, joint separately with Petyt and Wise. Previously, Wise proved that C’(1/6) groups are cocompactly cubulated, which has illuminated their separability properties following work of Agol. However, the cubulabilty of non-metric small-cancellation groups has remained largely open. In joint work with Petyt, we define a class of spaces termed “richly branching flats” which can be used as a geometric obstruction to cocompact cubulation. Using richly branching flats, we produce the first example of a non-cocompactly cubulated C(6) group. In the opposite direction, in joint work with Wise, we define “strict C(6)” groups, which are a class of small-cancellation groups intermediate to C(6) and C(7). We do not cubulate these groups, but we show that they share several properties with cubulated (relatively) hyperbolic groups. In particular, we prove a convex cocompact core theorem for quasiconvex subgroups of strict C(6) groups.
Time: Thursday, 27/4, 16:00 (Note the special time)
Place: Ross 70
Speaker: Zachary Munro (Technion)
Title: Richly branching flats and strict small-cancellation
Abstract:
I will discuss two projects addressing cubulability of small-cancellation groups, joint separately with Petyt and Wise. Previously, Wise proved that C’(1/6) groups are cocompactly cubulated, which has illuminated their separability properties following work of Agol. However, the cubulabilty of non-metric small-cancellation groups has remained largely open. In joint work with Petyt, we define a class of spaces termed “richly branching flats” which can be used as a geometric obstruction to cocompact cubulation. Using richly branching flats, we produce the first example of a non-cocompactly cubulated C(6) group. In the opposite direction, in joint work with Wise, we define “strict C(6)” groups, which are a class of small-cancellation groups intermediate to C(6) and C(7). We do not cubulate these groups, but we show that they share several properties with cubulated (relatively) hyperbolic groups. In particular, we prove a convex cocompact core theorem for quasiconvex subgroups of strict C(6) groups.