Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds
| 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.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.identifier.uri | https://hdl.handle.net/1794/19241 | |
| 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.discipline | Department of Mathematics | |
| thesis.degree.grantor | University of Oregon | |
| thesis.degree.level | doctoral | |
| thesis.degree.name | Ph.D. |
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