Inertia groups of high dimensional complex projective spaces

Abstract

For a complex projective space the inertia group, the homotopy inertia group and the concordance inertia group are isomorphic. In complex dimension 4n+1, these groups are related to computations in stable cohomotopy. Using stable homotopy theory, we make explicit computations to show that the inertia group is non-trivial in many cases. In complex dimension 9, we deduce some results on geometric structures on homotopy complex projective spaces and complex hyperbolic manifolds.

References in corpus (1)

• Farrell-Jones spheres and inertia groups of complex projective spaces

Cited by in corpus (2)

• Inertia Groups and Smooth Structures on Quaternionic Projective Spaces
• Smooth Structures on the product of 3-connected 8-manifolds with spheres