On Fredholm index, transversal approximations and Quillen's geometric complex cobordism of Hilbert manifolds with some applications to flag varieties of loop groups

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dc.contributor.authorÖzel, Cenap
dc.date.accessioned2021-06-23T18:54:18Z
dc.date.available2021-06-23T18:54:18Z
dc.date.issued2006
dc.departmentBAİBÜ, Fen Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractIn [Contemp. Math. 258 (2000) 1-19], by using Fredholm index we developed a version of Quillen's geometric cobordism theory for infinite dimensional Hilbert manifolds. This cobordism theory has a graded group structure under topological union operation and has push-forward maps for complex orientable Fredholm maps. In this work, by using Quinn's Transversality Theorem [Proc. Sympos. Pure. Math. 15 (1970) 213-222], it will be shown that this cobordism theory has a graded ring structure under transversal intersection operation and has pull-back maps for smooth maps. It will be shown that the Thom isomorphism in this theory will be satisfied for finite dimensional vector bundles over separable Hilbert manifolds and the projection formula for Gysin maps will be proved. After we discuss the relation between this theory and classical cobordism, we describe some applications to the complex cobordism of flag varieties of loop groups and we do some calculations. © 2005 Elsevier B.V. All rights reserved.en_US
dc.description.sponsorshipAbant Izzet Baysal Üniversitesi, AIBÜ: 2000/03/04/67en_US
dc.description.sponsorshipWe are indebted to Unit of Research and Developing, Bolu Abant Izzet Baysal University for their financial support during our project with numbered 2000/03/04/67. I would like to thank A.J. Baker and Department of Mathematics, University of Glasgow for personal support, conservations and hospitality.en_US
dc.identifier.doi10.1016/j.topol.2005.05.001
dc.identifier.endpage1525en_US
dc.identifier.issn0166-8641
dc.identifier.issue9en_US
dc.identifier.scopus2-s2.0-33644586705en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage1507en_US
dc.identifier.urihttps://doi.org/10.1016/j.topol.2005.05.001
dc.identifier.urihttps://hdl.handle.net/20.500.12491/4362
dc.identifier.volume153en_US
dc.identifier.wosWOS:000236257300010en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorÖzel, Cenap
dc.language.isoenen_US
dc.relation.ispartofTopology and its Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectCobordismen_US
dc.subjectFlag Varietyen_US
dc.subjectFredholm Mapen_US
dc.subjectHilbert Manifolden_US
dc.subjectLoop Groupen_US
dc.subjectTransversal Approximationsen_US
dc.titleOn Fredholm index, transversal approximations and Quillen's geometric complex cobordism of Hilbert manifolds with some applications to flag varieties of loop groupsen_US
dc.typeArticleen_US

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