The Thom isomorphism for nonorientable bundles
Identifieur interne : 002418 ( Istex/Corpus ); précédent : 002417; suivant : 002419The Thom isomorphism for nonorientable bundles
Auteurs : E. G. SklyarenkoSource :
- Journal of Mathematical Sciences [ 1072-3374 ] ; 2006-08-01.
Abstract
Abstract: The classical theory of Thom isomorphisms is extended to nonorientable vector bundles. The properties of orientation sheaves of bundles and of the Thom and Euler classes τ and e with respect to projections, fiber maps, Cartesian products, and Whitney sums of bundles are studied. The validity of standard constructions used in the applications of the classes τ and e is confirmed. It is shown that the Thom isomorphisms, together with their form, are consequences of the Poincaré duality.
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DOI: 10.1007/s10958-006-0226-3
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The properties of orientation sheaves of bundles and of the Thom and Euler classes <Emphasis Type="Italic">τ</Emphasis> and <Emphasis Type="Italic">e</Emphasis> with respect to projections, fiber maps, Cartesian products, and Whitney sums of bundles are studied. The validity of standard constructions used in the applications of the classes <Emphasis Type="Italic">τ</Emphasis> and <Emphasis Type="Italic">e</Emphasis> is confirmed. It is shown that the Thom isomorphisms, together with their form, are consequences of the Poincaré duality.</Para></Abstract><ArticleNote Type="Misc"><SimplePara>__________</SimplePara><SimplePara>Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 4, pp. 55–103, 2003.</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>The Thom isomorphism for nonorientable bundles</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>The Thom isomorphism for nonorientable bundles</title></titleInfo><name type="personal"><namePart type="given">E.</namePart><namePart type="given">G.</namePart><namePart type="family">Sklyarenko</namePart><affiliation>Department of Higher Geometry and Topology, Faculty Mechanics and Mathematics, Moscow State University, Leninskie gory, 119992, Moscow, Russia</affiliation><affiliation>E-mail: egskl@nw.math.msu.su</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Kluwer Academic Publishers-Consultants Bureau</publisher><place><placeTerm type="text">New York</placeTerm></place><dateIssued encoding="w3cdtf">2006-08-01</dateIssued><dateIssued encoding="w3cdtf">2006</dateIssued><copyrightDate encoding="w3cdtf">2006</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: The classical theory of Thom isomorphisms is extended to nonorientable vector bundles. The properties of orientation sheaves of bundles and of the Thom and Euler classes τ and e with respect to projections, fiber maps, Cartesian products, and Whitney sums of bundles are studied. The validity of standard constructions used in the applications of the classes τ and e is confirmed. 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