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 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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Department of Mathematics

Grantor dc:publisher

University of Oregon

Year dc:date.issued

2015

Author dc:creator

• Perlmutter, Nathan

Advisor dc:contributor.advisor

• Botvinnik, Boris

• Algebraic topology
• Diffeomorphism groups
• Differential topology
• Singularity Theory
• Surgery Theory

Statement dc:rights

• All Rights Reserved.

Language dc:language.iso

en_US

Handle dc:identifier.uri

https://hdl.handle.net/1794/19241

OAI record oai:identifier

https://scholarsbank.uoregon.edu/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Ascholarsbank.uoregon.edu%3A1794%2F19241