Inertia groups and smooth structures on quaternionic projective spaces
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Samik Basu
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.
Acknowledgements
The research of the first author was partially supported by NBHM (project ref. number 2/48(11)/2015/NBHM(R.P.)/R&D II/3743).
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Articles in the same Issue
- Frontmatter
- On the variance of the nodal volume of arithmetic random waves
- On length densities
- On weighted compactness of commutators of bilinear maximal Calderón–Zygmund singular integral operators
- Geometric nilpotent Lie algebras and zero-dimensional simple complete intersection singularities
- On cutting blocking sets and their codes
- Inertia groups and smooth structures on quaternionic projective spaces
- On the number of zeros of diagonal quartic forms over finite fields
- Weak martingale Hardy-type spaces associated with quasi-Banach function lattice
- A dual version of Huppert's ρ-σ conjecture for character codegrees
- A topological correspondence between partial actions of groups and inverse semigroup actions
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Articles in the same Issue
- Frontmatter
- On the variance of the nodal volume of arithmetic random waves
- On length densities
- On weighted compactness of commutators of bilinear maximal Calderón–Zygmund singular integral operators
- Geometric nilpotent Lie algebras and zero-dimensional simple complete intersection singularities
- On cutting blocking sets and their codes
- Inertia groups and smooth structures on quaternionic projective spaces
- On the number of zeros of diagonal quartic forms over finite fields
- Weak martingale Hardy-type spaces associated with quasi-Banach function lattice
- A dual version of Huppert's ρ-σ conjecture for character codegrees
- A topological correspondence between partial actions of groups and inverse semigroup actions
- On homotopy braids
- Holomorphic convexity of pseudoconvex spaces in terms of the rank of structural sheaf
- The Shintani double zeta functions
- Homological dimensions relative to preresolving subcategories II
- Simplicity of indecomposable set-theoretic solutions of the Yang–Baxter equation
- A converse theorem for quasimodular forms
