Speaker: Ryan Budney (University of Victoria, CA)

Abstract: I will describe Smale's proof that Diff(S^2) has the homotopy-type of O_3.  Then Cerf's re-imagining of Smale's proof. Cerf's version avoids Smale's usage of the Poincare-Bendixson theorem.  Lastly I will describe how Cerf's proof allows us to argue the Schoenflies monoid (isotopy classes of embedded, oriented co-dimension one spheres in S^n with the connect-sum operation) is a group for all n>=2.