Abstract

The work of Kervaire and Milnor reduces the classification of homotopy spheres in dimension atleast 5 to the problem of computing stable homotopy groups of spheres and their Kervaireinvariants. We will give an introduction to the recent developments in homotopy theory which leadsto the solution of the Kervaire invariant one problem and classification of homotopy spheres up toaround dimension 170.