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Generalized Snaith Splittings

dc.contributor.advisorBödigheimer, Carl-Friedrich
dc.contributor.authorWang, Juan
dc.date.accessioned2020-04-13T21:48:51Z
dc.date.available2020-04-13T21:48:51Z
dc.date.issued05.02.2009
dc.identifier.urihttp://hdl.handle.net/20.500.11811/4031
dc.description.abstractA Segal Γ-space A gives a homotopy functor A(X) and a connective homology theory h*(X;A) = π*(A(X)). The infinite symmetric product SP(X) and the configuration space C(R;X) ≅ Q(X) are well-known examples of Segal Γ-spaces; the former giving singular homology H*(X;Z) and the latter stable homotopy theory as their homotopy groups. Here we are concerned with another important example, the Segal Γ-space K leading to connective KO-theory: π*K(X) = ̃ko(X).
Like the first two examples, such functors A come very often with a filtration An(X) which splits after applying another suitable homotopy functor, perhaps even a Segal Γ-space B; in the first two examples one can take B = A and obtain the well-known Dold-Puppe splitting of SP(X) resp. the Snaith splitting of Q(X). Our main result is a splitting of K(X) using the functor B(X+) ≅ Ω∞-1(MO∧X+) representing unoriented cobordism, namely

B(K(X)+) ≅ B(V n=o Kn(X)/Kn-1(X)).

dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subject.ddc510 Mathematik
dc.titleGeneralized Snaith Splittings
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5N-16683
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID1668
ulbbnediss.date.accepted2008-12-19
ulbbnediss.instituteMathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Mathematisches Institut
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeTillmann, Ulrike


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