dc.contributor.author Erdal, M. A. en_US dc.date.accessioned 2019-02-21T16:02:04Z dc.date.available 2019-02-21T16:02:04Z dc.date.issued 2017-11-22 en_US dc.identifier.issn 0166-8641 dc.identifier.uri http://hdl.handle.net/11693/49959 dc.description.abstract In this paper we study M(X), the set of diffeomorphism classes of smooth manifolds with the simple homotopy type of X, via a map Ψ from M(X) into the quotient of K(X)=[X,BSO] by the action of the group of homotopy classes of simple self equivalences of X. The map Ψ describes which bundles over X can occur as normal bundles of manifolds in M(X). We determine the image of Ψ when X belongs to a certain class of homology spheres. In particular, we find conditions on elements of K(X) that guarantee they are pullbacks of normal bundles of manifolds in M(X). dc.language.iso English dc.source.title Topology and its Applications en_US dc.relation.isversionof https://doi.org/10.1016/j.topol.2017.11.006 dc.subject Cobordism en_US dc.subject Homology sphere en_US dc.subject K-theory en_US dc.subject Poincaré duality en_US dc.subject Spectral sequence en_US dc.title On smooth manifolds with the homotopy type of a homology sphere en_US dc.type Article en_US dc.department Department of Mathematics en_US dc.citation.spage 82 en_US dc.citation.epage 91 en_US dc.citation.volumeNumber 234 en_US dc.identifier.doi 10.1016/j.topol.2017.11.006 dc.publisher Elsevier dc.embargo.release 2020-02-01 en_US
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