A Cartan-Hadamard type theorem for relatively hyperbolic groups

Curtis Kent (NYU)

Abstract: Asymptotic cones are one way to formalize the idea of looking at a space from infinitely far away and provide a rich setting for the study of groups. I will give several examples of finitely generated groups with non-homeomorphic asymptotic cones (even with locally non-homeomorphic asymptotic cones). I will discuss the asymptotic cones of relatively hyperbolic groups and present a Cartan-Hadamard type theorem for relatively hyperbolic groups. Some of what I will talk about is joint work with Remi Coulon and Michael Hull.