MATH 7520: Berstein Seminar in Topology: subgroups of non-positively curved groups (Spring 2011)

Instructor: Tim Riley

“Hic etiam homines magna cornua habentes longitudine quatuor pedum, et sunt etiam serpentes tante magnitudinis, ut unum bovem comedant integrum.” Borgia map (c. 1430 AD), Vatican Library.

We will survey the subgroup structure of groups that are non-positively curved in senses such as CAT(0), CAT(–1), and hyperbolic — apparently benign classes of groups that can harbour geometric and computational wildness in their subgroups.

Likely topics include Dehn functions, distortion, the Rips Construction, Mihailova's Construction, Bestvina-Brady groups, Cannon-Thurston maps, and the apparent ubiquity of surface subgroups.

There are no prerequisites for attending this seminar other than a willingness to participate. Our findings may be disseminated via notes or a blog.