Inertia groups and smooth structures on quaternionic projective spaces

Abstract

Abstract This paper deals with certain results on the number of smooth structures on quaternionic projective spaces, obtained through the computation of inertia groups and their analogues, which in turn are computed using techniques from stable homotopy theory. 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.