The Kervaire invariant problem

Mike Hopkins, Harvard University
Fine Hall 314

The of existence of framed manifolds of Kervaire invariant one is one of the oldest unresolved problems in algebraic topology.  Important questions about smooth structures on spheres  and on the homotopy groups of spheres depend on its solution.  In this talk I will describe joint work with Mike Hill and Doug Ravenel which solves this problem in all dimensions except 126.