Characteristic Classes
Identifieur interne : 000523 ( Istex/Corpus ); précédent : 000522; suivant : 000524Characteristic Classes
Auteurs : Anastasios MalliosSource :
- Mathematics and Its Applications ; 1998.
Abstract
Abstract: We consider below (Chern) characteristic classes of vector sheaves, the analogue in our case of the same classes of vector bundles (over a C∞-manifold). In particular, we apply the counterpart here of the (differential- geometric) Chern-Weil description of these classes, in terms of the curvature (tensor). So, as happens in the standard case, the Bianchi identity (see the previous Chapter, Theorem 7.1) becomes here a key-result. On the other hand, one has to assume further, within this abstract treatment, the existence of an appropriate analogue of de Rham’s complex, to ensure, by analogy with the standard case, a cohomology class, which is thus (canonically) associated with any given “closed form”. So we start with the necessary preliminary material.
Url:
DOI: 10.1007/978-94-011-5006-4_4
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In particular, we apply the counterpart here of the (differential- geometric) Chern-Weil description of these classes, in terms of the curvature (tensor). So, as happens in the standard case, the Bianchi identity (see the previous Chapter, Theorem 7.1) becomes here a key-result. On the other hand, one has to assume further, within this abstract treatment, the existence of an appropriate analogue of de Rham’s complex, to ensure, by analogy with the standard case, a cohomology class, which is thus (canonically) associated with any given “closed form”. 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In particular, we apply the counterpart here of the (differential- geometric) <Emphasis Type="Italic">Chern-Weil description</Emphasis> of these classes, <Emphasis Type="Italic">in terms of the curvature</Emphasis> (tensor). So, as happens in the standard case, the <Emphasis Type="Italic">Bianchi identity</Emphasis> (see the previous Chapter, Theorem 7.1) becomes here a key-result. On the other hand, one has to assume further, within this abstract treatment, the existence of an <Emphasis Type="Italic">appropriate analogue of de Rham’s complex</Emphasis>, to ensure, by analogy with the standard case, a cohomology class, which is thus (canonically) associated with any given <Emphasis Type="Italic">“closed form”</Emphasis>. So we start with the necessary preliminary material.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Characteristic Classes</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Characteristic Classes</title></titleInfo><name type="personal"><namePart type="given">Anastasios</namePart><namePart type="family">Mallios</namePart><affiliation>Department of Mathematics, University of Athens, Athens, Greece</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="research-article" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Springer Netherlands</publisher><place><placeTerm type="text">Dordrecht</placeTerm></place><dateIssued encoding="w3cdtf">1998</dateIssued><dateIssued encoding="w3cdtf">1998</dateIssued><copyrightDate encoding="w3cdtf">1998</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: We consider below (Chern) characteristic classes of vector sheaves, the analogue in our case of the same classes of vector bundles (over a C∞-manifold). 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