In 1978, using Milnor's descriptions of exotic spheres, Gromoll and Meyer showed that there is a biquotient G//H which is diffemorohpic to an exotic sphere. Because a bi-invariant metric on G gives rise to a submersion metric on G//H, this proved the Gromoll-Meyer Sphere has a metric of nonnegative curvature, the first known metric on any exotic sphere to have nonnegative curvature.

The first part of my talk with cover Milnor's descriptions of exotic spheres while the second will focus on Gromoll and Meyer's construction as well as the inherited curavture properties (the bi-invariant metric actually induces a metric on G//H with quasi-positive curvature).