Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds
Let n > 1. We prove a homological stability theorem for the diffeomorphism groups of (4n+1)-dimensional manifolds, with respect to forming the connected sum with (2n-1)-connected, (4n+1)-dimensional manifolds that are stably parallelizable. Our techniques involve the study of the a...
| Main Author: | |
|---|---|
| Other Authors: | |
| Language: | en_US |
| Published: |
University of Oregon
2015
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1794/19241 |
| Summary: | Let n > 1. We prove a homological stability theorem for the
diffeomorphism groups of (4n+1)-dimensional manifolds, with respect
to forming the connected sum with (2n-1)-connected,
(4n+1)-dimensional manifolds that are stably parallelizable.
Our techniques involve the study of the action of the diffeomorphism group of a manifold M on the linking form associated to the homology groups of M.
In order to study this action we construct a geometric model for the linking form using the intersections of embedded and immersed Z/k-manifolds.
In addition to our main homological stability theorem, we prove several results regarding disjunction for embeddings and immersions of Z/k-manifolds that could be of independent interest. |
|---|