dc.contributor.author | Annfelt Moe, Haaken | nb_NO |
dc.date.accessioned | 2014-12-19T14:00:06Z | |
dc.date.available | 2014-12-19T14:00:06Z | |
dc.date.created | 2013-04-17 | nb_NO |
dc.date.issued | 2012 | nb_NO |
dc.identifier | 616486 | nb_NO |
dc.identifier.isbn | 978-82-471-3462-7 (printed ver.) | nb_NO |
dc.identifier.isbn | 978-82-471-3463-4 (electronic ver.) | nb_NO |
dc.identifier.uri | http://hdl.handle.net/11250/259140 | |
dc.description.abstract | In this dissertation some ad theories and their relation to certain spectra are investigated. Quinn defined bordism-type theories, semisimplicial constructions with a geometric realization that is an Ω -spectrum. Here we study Laures and McClure’s ad theories, a strengthening of the axioms of the bordism-type theories. Associated to an ad theory is a Quinn spectrum, an Ω-spectrum that is the geometric realization of a semisiplicial set coming fromthe ad theory.
The goal of the dissertation is to show equivalences between on one hand the Thom spectrum MSO and the Madsen-Tillmann spectra MT+ (d) and on the other hand some constructed Quinn spectra. This is done working through the singular complex of MSO and MT+ (d).
Transversality is important here. The final step of the comparison of spectra is done by comparing the subset of the singular complex that is transversal to the 0- section of the spaces of the spectra MSO and MT+ (d) to the semisimplicial sets coming from the ad theories. For MSO, that this is an equivalence is a simplicial version of part of Rene Thoms proof about the stable homotopy of MSO.
The ad theories are functors from index categories that come from ball complexes, to a target category we construct. This target category is built out of embedded smooth compactmanifolds with corners. | nb_NO |
dc.language | eng | nb_NO |
dc.publisher | Norges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fag | nb_NO |
dc.relation.ispartofseries | Doktoravhandlinger ved NTNU, 1503-8181; 2012:93 | nb_NO |
dc.title | Constructing Certain Spectra from Ad Theories | nb_NO |
dc.type | Doctoral thesis | nb_NO |
dc.contributor.department | Norges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fag | nb_NO |
dc.description.degree | PhD i matematiske fag | nb_NO |
dc.description.degree | PhD in Mathematical Sciences | en_GB |