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.
| Identifer | oai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/19241 |
| Date | 18 August 2015 |
| Creators | Perlmutter, Nathan |
| Contributors | Botvinnik, Boris |
| Publisher | University of Oregon |
| Source Sets | University of Oregon |
| Language | en_US |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Rights | All Rights Reserved. |
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