Eine Spektralsequenz in der stetigen Kohomologietheorie topologischer Gruppen
Identifieur interne : 001A85 ( Istex/Corpus ); précédent : 001A84; suivant : 001A86Eine Spektralsequenz in der stetigen Kohomologietheorie topologischer Gruppen
Auteurs : Andreas StieglitzSource :
- manuscripta mathematica [ 0025-2611 ] ; 1975-06-01.
Abstract
Abstract: Let H*(G; M) be the continuous cohomology of a locally compact group G with coefficients in a topological RG-module M. If G operates without fixed points on a R-paracompact space X such that there is a slice through each point and X/G is R-paracompact, then there exists a spectral sequence converging to the equivariant cohomology H*(X,G; M) of X with second term E2 p.q≅Hp(G; HqX; M)) where the sheaf theoretical cohomology of X is suitable topologized. Several applications and a generalization to actions of G with non-empty fixed point sets are given.
Url:
DOI: 10.1007/BF01181638
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If G operates without fixed points on a R-paracompact space X such that there is a slice through each point and X/G is R-paracompact, then there exists a spectral sequence converging to the equivariant cohomology H*(X,G; M) of X with second term E2 p.q≅Hp(G; HqX; M)) where the sheaf theoretical cohomology of X is suitable topologized. Several applications and a generalization to actions of G with non-empty fixed point sets are given.</div></front></TEI><istex><corpusName>springer-journals</corpusName><author><json:item><name>Andreas Stieglitz</name><affiliations><json:string>Mathematisches Institut, der Ruhr-Universität Bochum, Universitätsstraße 150, D 463, Bochum</json:string></affiliations></json:item></author><articleId><json:string>BF01181638</json:string><json:string>Art4</json:string></articleId><arkIstex>ark:/67375/1BB-5B2QD7RR-J</arkIstex><language><json:string>ger</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: Let H*(G; M) be the continuous cohomology of a locally compact group G with coefficients in a topological RG-module M. 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If G operates without fixed points on a R-paracompact space X such that there is a slice through each point and X/G is R-paracompact, then there exists a spectral sequence converging to the equivariant cohomology H*(X,G; M) of X with second term E2 p.q≅Hp(G; HqX; M)) where the sheaf theoretical cohomology of X is suitable topologized. Several applications and a generalization to actions of G with non-empty fixed point sets are given.</p></abstract><textClass><keywords scheme="Journal Subject"><list><head>Mathematics</head><item><term>Mathematics, general</term></item><item><term>Algebraic Geometry</term></item><item><term>Topological Groups, Lie Groups</term></item><item><term>Geometry</term></item><item><term>Number Theory</term></item><item><term>Calculus of Variations and Optimal Control</term></item><item><term>Optimization</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1975-03-24">Created</change><change when="1975-06-01">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-11-30">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/82FF7F8F0ED590C8CDBA6EBBC628DA25F3EEB96C/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus springer-journals not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//Springer-Verlag//DTD A++ V2.4//EN" URI="http://devel.springer.de/A++/V2.4/DTD/A++V2.4.dtd" name="istex:docType"></istex:docType><istex:document><Publisher><PublisherInfo><PublisherName>Springer-Verlag</PublisherName><PublisherLocation>Berlin/Heidelberg</PublisherLocation></PublisherInfo><Journal><JournalInfo JournalProductType="ArchiveJournal" NumberingStyle="Unnumbered"><JournalID>229</JournalID><JournalPrintISSN>0025-2611</JournalPrintISSN><JournalElectronicISSN>1432-1785</JournalElectronicISSN><JournalTitle>manuscripta mathematica</JournalTitle><JournalAbbreviatedTitle>Manuscripta Math</JournalAbbreviatedTitle><JournalSubjectGroup><JournalSubject Type="Primary">Mathematics</JournalSubject><JournalSubject Type="Secondary">Mathematics, general</JournalSubject><JournalSubject Type="Secondary">Algebraic Geometry</JournalSubject><JournalSubject Type="Secondary">Topological Groups, Lie Groups</JournalSubject><JournalSubject Type="Secondary">Geometry</JournalSubject><JournalSubject Type="Secondary">Number Theory</JournalSubject><JournalSubject Type="Secondary">Calculus of Variations and Optimal Control</JournalSubject><JournalSubject Type="Secondary">Optimization</JournalSubject></JournalSubjectGroup></JournalInfo><Volume><VolumeInfo VolumeType="Regular" TocLevels="0"><VolumeIDStart>16</VolumeIDStart><VolumeIDEnd>16</VolumeIDEnd><VolumeIssueCount>4</VolumeIssueCount></VolumeInfo><Issue IssueType="Regular"><IssueInfo TocLevels="0"><IssueIDStart>2</IssueIDStart><IssueIDEnd>2</IssueIDEnd><IssueArticleCount>6</IssueArticleCount><IssueHistory><CoverDate><DateString>1975</DateString><Year>1975</Year><Month>6</Month></CoverDate></IssueHistory><IssueCopyright><CopyrightHolderName>Springer-Verlag</CopyrightHolderName><CopyrightYear>1975</CopyrightYear></IssueCopyright></IssueInfo><Article ID="Art4"><ArticleInfo Language="De" ArticleType="OriginalPaper" NumberingStyle="Unnumbered" TocLevels="0" ContainsESM="No"><ArticleID>BF01181638</ArticleID><ArticleDOI>10.1007/BF01181638</ArticleDOI><ArticleSequenceNumber>4</ArticleSequenceNumber><ArticleTitle Language="De">Eine Spektralsequenz in der stetigen Kohomologietheorie topologischer Gruppen</ArticleTitle><ArticleFirstPage>151</ArticleFirstPage><ArticleLastPage>168</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2005</Year><Month>1</Month><Day>31</Day></RegistrationDate><Received><Year>1975</Year><Month>3</Month><Day>24</Day></Received></ArticleHistory><ArticleCopyright><CopyrightHolderName>Springer-Verlag</CopyrightHolderName><CopyrightYear>1975</CopyrightYear></ArticleCopyright><ArticleGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ArticleGrants><ArticleContext><JournalID>229</JournalID><VolumeIDStart>16</VolumeIDStart><VolumeIDEnd>16</VolumeIDEnd><IssueIDStart>2</IssueIDStart><IssueIDEnd>2</IssueIDEnd></ArticleContext></ArticleInfo><ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Andreas</GivenName><FamilyName>Stieglitz</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgDivision>Mathematisches Institut</OrgDivision><OrgName>der Ruhr-Universität Bochum</OrgName><OrgAddress><Street>Universitätsstraße 150</Street><Postcode>D 463</Postcode><City>Bochum</City></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>Let H<Superscript>*</Superscript>(G; M) be the continuous cohomology of a locally compact group G with coefficients in a topological RG-module M. If G operates without fixed points on a R-paracompact space X such that there is a slice through each point and X/G is R-paracompact, then there exists a spectral sequence converging to the equivariant cohomology H<Superscript>*</Superscript>(X,G; M) of X with second term E<Subscript>2</Subscript><Superscript>p.q</Superscript>≅H<Superscript>p</Superscript>(G; H<Superscript>q</Superscript>X; M)) where the sheaf theoretical cohomology of X is suitable topologized. Several applications and a generalization to actions of G with non-empty fixed point sets are given.</Para></Abstract></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="de"><title>Eine Spektralsequenz in der stetigen Kohomologietheorie topologischer Gruppen</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="de"><title>Eine Spektralsequenz in der stetigen Kohomologietheorie topologischer Gruppen</title></titleInfo><name type="personal"><namePart type="given">Andreas</namePart><namePart type="family">Stieglitz</namePart><affiliation>Mathematisches Institut, der Ruhr-Universität Bochum, Universitätsstraße 150, D 463, Bochum</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>Springer-Verlag</publisher><place><placeTerm type="text">Berlin/Heidelberg</placeTerm></place><dateCreated encoding="w3cdtf">1975-03-24</dateCreated><dateIssued encoding="w3cdtf">1975-06-01</dateIssued><dateIssued encoding="w3cdtf">1975</dateIssued><copyrightDate encoding="w3cdtf">1975</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">de</languageTerm><languageTerm type="code" authority="iso639-2b">ger</languageTerm></language><abstract lang="en">Abstract: Let H*(G; M) be the continuous cohomology of a locally compact group G with coefficients in a topological RG-module M. If G operates without fixed points on a R-paracompact space X such that there is a slice through each point and X/G is R-paracompact, then there exists a spectral sequence converging to the equivariant cohomology H*(X,G; M) of X with second term E2 p.q≅Hp(G; HqX; M)) where the sheaf theoretical cohomology of X is suitable topologized. Several applications and a generalization to actions of G with non-empty fixed point sets are given.</abstract><relatedItem type="host"><titleInfo><title>manuscripta mathematica</title></titleInfo><titleInfo type="abbreviated"><title>Manuscripta Math</title></titleInfo><genre type="journal" displayLabel="Archive Journal" authority="ISTEX" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><originInfo><publisher>Springer</publisher><dateIssued encoding="w3cdtf">1975-06-01</dateIssued><copyrightDate encoding="w3cdtf">1975</copyrightDate></originInfo><subject><genre>Mathematics</genre><topic>Mathematics, general</topic><topic>Algebraic Geometry</topic><topic>Topological Groups, Lie Groups</topic><topic>Geometry</topic><topic>Number Theory</topic><topic>Calculus of Variations and Optimal Control</topic><topic>Optimization</topic></subject><identifier type="ISSN">0025-2611</identifier><identifier type="eISSN">1432-1785</identifier><identifier type="JournalID">229</identifier><identifier type="IssueArticleCount">6</identifier><identifier type="VolumeIssueCount">4</identifier><part><date>1975</date><detail type="volume"><number>16</number><caption>vol.</caption></detail><detail type="issue"><number>2</number><caption>no.</caption></detail><extent unit="pages"><start>151</start><end>168</end></extent></part><recordInfo><recordOrigin>Springer-Verlag, 1975</recordOrigin></recordInfo></relatedItem><identifier type="istex">82FF7F8F0ED590C8CDBA6EBBC628DA25F3EEB96C</identifier><identifier type="ark">ark:/67375/1BB-5B2QD7RR-J</identifier><identifier type="DOI">10.1007/BF01181638</identifier><identifier type="ArticleID">BF01181638</identifier><identifier type="ArticleID">Art4</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag, 1975</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</recordContentSource><recordOrigin>Springer-Verlag, 1975</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/82FF7F8F0ED590C8CDBA6EBBC628DA25F3EEB96C/metadata/json</uri></json:item></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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