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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">A Bruhat decomposition for the loop space of a compact group: A new approach to results of Bott</title>
<author><name sortKey="Garland, Howard" sort="Garland, Howard" uniqKey="Garland H" first="Howard" last="Garland">Howard Garland</name>
<affiliation><nlm:aff id="af1">Yale University, New Haven, Connecticut 06520</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Raghunathan, M S" sort="Raghunathan, M S" uniqKey="Raghunathan M" first="M. S." last="Raghunathan">M. S. Raghunathan</name>
<affiliation><nlm:aff id="af2">Columbia University, New York, N.Y. 10027</nlm:aff>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">PMC</idno>
<idno type="pmid">16592292</idno>
<idno type="pmc">388799</idno>
<idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC388799</idno>
<idno type="RBID">PMC:388799</idno>
<date when="1975">1975</date>
<idno type="wicri:Area/Pmc/Corpus">000042</idno>
<idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000042</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">A Bruhat decomposition for the loop space of a compact group: A new approach to results of Bott</title>
<author><name sortKey="Garland, Howard" sort="Garland, Howard" uniqKey="Garland H" first="Howard" last="Garland">Howard Garland</name>
<affiliation><nlm:aff id="af1">Yale University, New Haven, Connecticut 06520</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Raghunathan, M S" sort="Raghunathan, M S" uniqKey="Raghunathan M" first="M. S." last="Raghunathan">M. S. Raghunathan</name>
<affiliation><nlm:aff id="af2">Columbia University, New York, N.Y. 10027</nlm:aff>
</affiliation>
</author>
</analytic>
<series><title level="j">Proceedings of the National Academy of Sciences of the United States of America</title>
<idno type="ISSN">0027-8424</idno>
<idno type="eISSN">1091-6490</idno>
<imprint><date when="1975">1975</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass></textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en"><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>
</div>
</front>
</TEI>
<pmc article-type="research-article"><pmc-comment>The publisher of this article does not allow downloading of the full text in XML form.</pmc-comment>
<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>
</record>
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