Browsing Mathematics Theses and Dissertations by Subject "Algebraic topology"
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Kronholm, William C., 1980 (University of Oregon, June , 2008)[more][less]Kronholm, William C., 1980 20090113T00:36:10Z 20090113T00:36:10Z 200806 http://hdl.handle.net/1794/8284 x, 72 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. The theory of equivariant homology and cohomology was first created by Bredon in his 1967 paper and has since been developed and generalized by May, Lewis, Costenoble, and a host of others. However, there has been a notable lack of computations done. In this paper, a version of the Serre spectral sequence of a fibration is developed for RO ( G )graded equivariant cohomology of G spaces for finite groups G . This spectral sequence is then used to compute cohomology of projective bundles and certain loop spaces. In addition, the cohomology of Rep( G )complexes, with appropriate coefficients, is shown to always be free. As an application, the cohomology of real projective spaces and some Grassmann manifolds are computed, with an eye towards developing a theory of equivariant characteristic classes. Adviser: Daniel Dugger en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2008; Algebraic topology Equivariant topology Spectral sequence Serre spectral sequence Mathematics The RO(G)graded Serre Spectral Sequence Thesis

Leeman, Aaron, 1974 (University of Oregon, June , 2009)[more][less]Leeman, Aaron, 1974 20100301T23:23:03Z 20100301T23:23:03Z 200906 http://hdl.handle.net/1794/10227 vii, 34 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. We study the Bousfield localization functors known as [Special characters omitted], as described in [MahS]. In particular we would like to understand how they interact with suspension and how they stabilize. We prove that suitably connected [Special characters omitted]acyclic spaces have suspensions which are built out of a particular type n space, which is an unstable analog of the fact that [Special characters omitted]acyclic spectra are built out of a particular type n spectrum. This theorem follows DrorFarjoun's proof in the case n = 1 with suitable alterations. We also show that [Special characters omitted] applied to a space stabilizes in a suitable way to [Special characters omitted] applied to the corresponding suspension spectrum. Committee in charge: Hal Sadofsky, Chairperson, Mathematics; Arkady Berenstein, Member, Mathematics; Daniel Dugger, Member, Mathematics; Dev Sinha, Member, Mathematics; William Rossi, Outside Member, English en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2009; Chromatic functors Bousfield functors Acyclic spaces Suspension spectrum Algebraic topology Mathematics Stabilization of chromatic functors Thesis

Vicinsky, Deborah (University of Oregon, August 18, 2015)[more][less]Sadofsky, Hal Vicinsky, Deborah 20150818T23:06:22Z 20150818T23:06:22Z 20150818 http://hdl.handle.net/1794/19283 We construct categories of spectra for two model categories. The first is the category of small categories with the canonical model structure, and the second is the category of directed graphs with the BissonTsemo model structure. In both cases, the category of spectra is homotopically trivial. This implies that the Goodwillie derivatives of the identity functor in each category, if they exist, are weakly equivalent to the zero spectrum. Finally, we give an infinite family of model structures on the category of small categories. en_US University of Oregon All Rights Reserved. Algebraic topology Goodwillie calculus Homotopy theory Model categories The Homotopy Calculus of Categories and Graphs Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon
Now showing items 13 of 3