On smooth Chas-Sullivan loop product in Quillen's geometric complex cobordism of Hilbert manifolds

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dc.contributor.authorÖzel, Cenap
dc.date.accessioned2021-06-23T18:54:15Z
dc.date.available2021-06-23T18:54:15Z
dc.date.issued2006
dc.departmentBAİBÜ, Fen Edebiyat Fakültesi, Fizik Bölümüen_US
dc.description.abstractIn [A.J. Baker, C. Ozel, Complex cobordism of Hilbert manifolds with some applications to flag varieties, 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 [C. Ozel, On Fredholm index, transversal approximations and Quillen's geometric complex cobordism of Hilbert manifolds with some applications to flag varieties of loop groups, in preparation], by using Quinn's Transversality Theorem [F. Quinn, Transversal approximation on Banach manifolds, Proc. Sympos. Pure Math. 15 (1970) 213-222], it has been shown that this cobordism theory has a graded ring structure under transversal intersection operation and has pull-back maps for smooth maps. It has been shown that the Thom isomorphism in this theory was satisfied for finite dimensional vector bundles over separable Hilbert manifolds and the projection formula for Gysin maps has been proved. In [M. Chas, D. Sullivan, String topology, math.GT/9911159, 1999], Chas and Sullivan described an intersection product on the homology of loop space LM. In [R.L. Cohen, J.D.S. Jones, A homotopy theoretic realization of string topology, math.GT/0107187, 2001], R. Cohen and J. Jones described a realization of the Chas-Sullivan loop product in terms of a ring spectrum structure on the Thom spectrum of a certain virtual bundle over the loop space. In this paper, we will extend this product on cobordism and bordism theories. © 2005 Elsevier B.V. All rights reserved.en_US
dc.identifier.doi10.1016/j.topol.2005.08.004
dc.identifier.endpage2117en_US
dc.identifier.issn0166-8641
dc.identifier.issue12en_US
dc.identifier.scopus2-s2.0-33646820369en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage2104en_US
dc.identifier.urihttps://doi.org/10.1016/j.topol.2005.08.004
dc.identifier.urihttps://hdl.handle.net/20.500.12491/4340
dc.identifier.volume153en_US
dc.identifier.wosWOS:000238471700012en_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.subjectChas-Sullivan Loop Producten_US
dc.subjectCobordismen_US
dc.subjectFredholm Mapen_US
dc.subjectHilbert Manifolden_US
dc.subjectLoop Spaceen_US
dc.subjectPontrjagin-Thom Constructionen_US
dc.titleOn smooth Chas-Sullivan loop product in Quillen's geometric complex cobordism of Hilbert manifoldsen_US
dc.typeArticleen_US

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