Inertia groups and smooth structures on quaternionic projective spaces

Article Type

Research Article

Publication Title

Forum Mathematicum

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.

First Page

369

Last Page

383

DOI

10.1515/forum-2020-0125

Publication Date

3-1-2022

Comments

Open Access, Green

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