dc.contributor.advisor |
Botvinnik, Boris |
|
dc.contributor.author |
Perlmutter, Nathan |
|
dc.date.accessioned |
2015-08-18T23:01:18Z |
|
dc.date.available |
2015-08-18T23:01:18Z |
|
dc.date.issued |
2015-08-18 |
|
dc.identifier.uri |
http://hdl.handle.net/1794/19241 |
|
dc.description.abstract |
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. |
en_US |
dc.language.iso |
en_US |
|
dc.publisher |
University of Oregon |
|
dc.rights |
All Rights Reserved. |
|
dc.subject |
Algebraic topology |
en_US |
dc.subject |
Diffeomorphism groups |
en_US |
dc.subject |
Differential topology |
en_US |
dc.subject |
Singularity Theory |
en_US |
dc.subject |
Surgery Theory |
en_US |
dc.title |
Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds |
|
dc.type |
Electronic Thesis or Dissertation |
|
thesis.degree.name |
Ph.D. |
|
thesis.degree.level |
doctoral |
|
thesis.degree.discipline |
Department of Mathematics |
|
thesis.degree.grantor |
University of Oregon |
|