Classifying seven dimensional manifolds of fixed cohomology type Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/bk128f263

Descriptions

Attribute NameValues
Creator
Abstract or Summary
  • Finding new examples of compact simply connected spaces admitting a Riemannian metric of positive sectional curvature is a fundamental problem in differential geometry. Likewise, studying topological properties of families of manifolds is very interesting to topologists. The Eschenburg spaces combine both of those interests: they are positively curved Riemannian manifolds whose topological classification is known. There is a second family consisting of the Witten manifolds: they are the examples of compact simply connected spaces admitting Einstein metrics of positive Ricci curvature. Thirdly, there is a notion of generalized Witten manifold as well. Topologically, all three families share the same cohomology ring. This common ring structure motivates the definition of a manifold of type r, where r is the order of the fourth cohomology group. In 1991, M. Kreck and S. Stolz classified manifolds M of type r up to homeomorphism and dieomorphism using invariants s̄[subscript i](M) and s[subscript i](M), for i = 1, 2, 3. This gave rise to many new examples of nondieomorphic but homeomorphic manifolds. In this dissertation, new versions of the homeomorphism and dieomorphism classification of manifolds of type r are proven. In particular, we can replace s̄₁ and s̄₃ by the first Pontrjagin class and the self-linking number in the homeomorphism classification of spin manifolds of type r. As the formulas of the two latter invariants are in general much easier to compute, this simplifies the classification of these manifolds up to homeomorphism significantly.
Resource Type
Date Available
Date Copyright
Date Issued
Degree Level
Degree Name
Degree Field
Degree Grantor
Commencement Year
Advisor
Committee Member
Academic Affiliation
Non-Academic Affiliation
Keyword
Subject
Rights Statement
Peer Reviewed
Language
Replaces
Additional Information
  • description.provenance : Approved for entry into archive by Julie Kurtz(julie.kurtz@oregonstate.edu) on 2012-04-11T21:37:16Z (GMT) No. of bitstreams: 1 PongdateDissert.pdf: 527832 bytes, checksum: 3da86b02ad7569ca47ef91fa9ba4907d (MD5)
  • description.provenance : Approved for entry into archive by Laura Wilson(laura.wilson@oregonstate.edu) on 2012-04-11T23:15:18Z (GMT) No. of bitstreams: 1 PongdateDissert.pdf: 527832 bytes, checksum: 3da86b02ad7569ca47ef91fa9ba4907d (MD5)
  • description.provenance : Made available in DSpace on 2012-04-11T23:15:18Z (GMT). No. of bitstreams: 1 PongdateDissert.pdf: 527832 bytes, checksum: 3da86b02ad7569ca47ef91fa9ba4907d (MD5) Previous issue date: 2012-03-21
  • description.provenance : Submitted by Patricia Black (patricia.black@oregonstate.edu) on 2012-04-11T21:06:50Z No. of bitstreams: 1 PongdateDissert.pdf: 527832 bytes, checksum: 3da86b02ad7569ca47ef91fa9ba4907d (MD5)

Relationships

In Administrative Set:
Last modified: 08/20/2017

Downloadable Content

Download PDF
Citations:

EndNote | Zotero | Mendeley

Items