Inertia Groups and Smooth Structures on Quaternionic Projective Spaces

Abstract

For a quarternionic projective space, the homotopy inertia group and the concordance inertia group are isomorphic, but the inertia group might be different. We show that the concordance inertia group is trivial in dimension 20, but there are many examples in high dimensions where the concordance inertia group is non-trivial. We extend these to computations of concordance classes of smooth structures. These have applications to $3$-sphere actions on homotopy spheres and tangential homotopy structures.Comment: 13 page