A Bruhat decomposition for the loop space of a compact group: A new approach to results of Bott
Identifieur interne : 000022 ( Pmc/Checkpoint ); précédent : 000021; suivant : 000023A Bruhat decomposition for the loop space of a compact group: A new approach to results of Bott
Auteurs : Howard Garland [États-Unis] ; M. S. Raghunathan [États-Unis]Source :
- Proceedings of the National Academy of Sciences of the United States of America [ 0027-8424 ] ; 1975.
Abstract
We give a new proof of Bott's result, that the loop space of a compact, simply connected, simple Lie group has a cellular decomposition of a certain type. In particular, one obtains the Poincaré polynomial for the loop space and Bott periodicity for the unitary group.
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PubMed: 16592292
PubMed Central: 388799
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<front><journal-meta><journal-id journal-id-type="nlm-ta">Proc Natl Acad Sci U S A</journal-id><journal-title>Proceedings of the National Academy of Sciences of the United States of America</journal-title><issn pub-type="ppub">0027-8424</issn><issn pub-type="epub">1091-6490</issn></journal-meta><article-meta><article-id pub-id-type="pmid">16592292</article-id><article-id pub-id-type="pmc">388799</article-id><article-categories><subj-group subj-group-type="heading"><subject>Physical Sciences: Mathematics</subject></subj-group></article-categories><title-group><article-title>A Bruhat decomposition for the loop space of a compact group: A new approach to results of Bott</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Garland</surname><given-names>Howard</given-names></name><xref ref-type="aff" rid="af1">*</xref></contrib><contrib contrib-type="author"><name><surname>Raghunathan</surname><given-names>M. S.</given-names></name><xref ref-type="aff" rid="af2">†</xref></contrib></contrib-group><aff id="af1"><label>*</label>Yale University, New Haven, Connecticut 06520</aff><aff id="af2"><label>†</label>Columbia University, New York, N.Y. 10027</aff><aff id="af3"><label></label>Tata Institute of Fundamental Research, Bombay, India</aff><pub-date pub-type="ppub"><month>12</month><year>1975</year></pub-date><volume>72</volume><issue>12</issue><fpage>4716</fpage><lpage>4717</lpage><abstract><p>We give a new proof of Bott's result, that the loop space of a compact, simply connected, simple Lie group has a cellular decomposition of a certain type. In particular, one obtains the Poincaré polynomial for the loop space and Bott periodicity for the unitary group.</p></abstract><kwd-group><kwd>Bott periodicity</kwd><kwd>loop spaces</kwd><kwd>Bruhat cells</kwd><kwd>Lie groups</kwd><kwd>cohomology</kwd></kwd-group></article-meta></front></pmc><affiliations><list><country><li>États-Unis</li></country><region><li>Connecticut</li><li>État de New York</li></region><settlement><li>New York</li></settlement><orgName><li>Université Columbia</li></orgName></list><tree><country name="États-Unis"><region name="Connecticut"><name sortKey="Garland, Howard" sort="Garland, Howard" uniqKey="Garland H" first="Howard" last="Garland">Howard Garland</name></region><name sortKey="Raghunathan, M S" sort="Raghunathan, M S" uniqKey="Raghunathan M" first="M. S." last="Raghunathan">M. S. Raghunathan</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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