Title: Relative Cubulation of Small Cancellation Quotients
Speaker: Teddy Einstein (University of Pittsburgh)
Abstract: Daniel Groves and I introduced relatively geometric actions, a new kind of action of a relatively hyperbolic group on a CAT(0) cube complex. Building on results of Martin and Steenbock for properly and cocompactly cubulated groups, Thomas Ng and I proved that C’(1/6)--small cancellation free products of relatively cubulable groups are relatively cubulable. The flexibility of relatively geometric actions allowed us to prove that C’(1/6)--small cancellation free products of residually finite groups are residually finite – without any need to assume that the factors are cubulable. In this talk, I will discuss techniques used to produce relatively geometric cubulations, applications to small cancellation quotients and potential future applications to random groups and small cancellation quotients of relatively hyperbolic groups.