Sommer, Oliver Carsten; Sommer, Oliver: The diffeomorphism group of an exotic sphere. 2017
Inhalt
- Notation
- Introduction
- Preliminaries
- The spaces O, TOP and G
- Pseudo smooth structures on spheres
- Exotic spheres and the surgery exact sequence
- Multiplicative structures on the sphere
- Homotopy orbits, fixed points and the Tate construction
- The real K-theory spectrum
- Statement of results
- Obstructions to the lifting question
- First obstruction: Lifting to the group of homeomorphisms
- Second obstruction: Lifting to the group of diffeomorphisms
- A homotopy operation
- Extension to the category of spaces
- Extension to the category of spectra
- Relation to the second obstruction
- The formulation in dimension seven
- A reformulation employing a lift to quadratic L-theory
- An approximation of G(n)/TOP(n)
- An approximation of TOP(n)/O(n)
- An attempted calculation using bo
- The approximation using topological K-theory
- The simplification as homotopy fiber in dimension seven
- A functional cohomology operation for the completed real K-theory spectrum
- The image of the eight homology of the cofiber of eta
- Discussion
- Appendix
- References