Positive Curvature, Macroscopic Dimension, Spectral Gaps and Higher Signatures
Identifieur interne : 002B35 ( Istex/Curation ); précédent : 002B34; suivant : 002B36Positive Curvature, Macroscopic Dimension, Spectral Gaps and Higher Signatures
Auteurs : M. Gromov [France, États-Unis]Source :
- Progress in Mathematics ; 1996.
Abstract
Abstract: Our journey starts with a macroscopic view of Riemannian manifolds with positive scalar curvature and terminates with a glimpse of the proof of the homotopy invariance of some Novikov higher signatures of non-simply connected manifolds. Our approach focuses on the spectra of geometric differential operators on compact and non-compact manifolds V where the link with the macroscopic geometry and topology is established with suitable index theorems for our operators twisted with almost flat bundles over V. Our perspective mainly comes from the asymptotic geometry of infinite groups and foliations.
Url:
DOI: 10.1007/978-1-4612-4098-3_1
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: Pour aller vers cette notice dans l'étape Curation :002B35
Links to Exploration step
ISTEX:D2681EB71F482A0EE9F8A12F1D8802C623FC24C6Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Positive Curvature, Macroscopic Dimension, Spectral Gaps and Higher Signatures</title>
<author><name sortKey="Gromov, M" sort="Gromov, M" uniqKey="Gromov M" first="M." last="Gromov">M. Gromov</name>
<affiliation wicri:level="1"><mods:affiliation>Institut des Hautes Etudes Scientifiques, 35 Route de Chartres, 91440, Bures-sur-Yvette, France</mods:affiliation>
<country xml:lang="fr">France</country>
<wicri:regionArea>Institut des Hautes Etudes Scientifiques, 35 Route de Chartres, 91440, Bures-sur-Yvette</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1"><mods:affiliation>University of Maryland, 20742, College Park, MD, USA</mods:affiliation>
<country xml:lang="fr">États-Unis</country>
<wicri:regionArea>University of Maryland, 20742, College Park, MD</wicri:regionArea>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:D2681EB71F482A0EE9F8A12F1D8802C623FC24C6</idno>
<date when="1996" year="1996">1996</date>
<idno type="doi">10.1007/978-1-4612-4098-3_1</idno>
<idno type="url">https://api.istex.fr/document/D2681EB71F482A0EE9F8A12F1D8802C623FC24C6/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">002B35</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002B35</idno>
<idno type="wicri:Area/Istex/Curation">002B35</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Positive Curvature, Macroscopic Dimension, Spectral Gaps and Higher Signatures</title>
<author><name sortKey="Gromov, M" sort="Gromov, M" uniqKey="Gromov M" first="M." last="Gromov">M. Gromov</name>
<affiliation wicri:level="1"><mods:affiliation>Institut des Hautes Etudes Scientifiques, 35 Route de Chartres, 91440, Bures-sur-Yvette, France</mods:affiliation>
<country xml:lang="fr">France</country>
<wicri:regionArea>Institut des Hautes Etudes Scientifiques, 35 Route de Chartres, 91440, Bures-sur-Yvette</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1"><mods:affiliation>University of Maryland, 20742, College Park, MD, USA</mods:affiliation>
<country xml:lang="fr">États-Unis</country>
<wicri:regionArea>University of Maryland, 20742, College Park, MD</wicri:regionArea>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="s">Progress in Mathematics</title>
<imprint><date>1996</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Abstract: Our journey starts with a macroscopic view of Riemannian manifolds with positive scalar curvature and terminates with a glimpse of the proof of the homotopy invariance of some Novikov higher signatures of non-simply connected manifolds. Our approach focuses on the spectra of geometric differential operators on compact and non-compact manifolds V where the link with the macroscopic geometry and topology is established with suitable index theorems for our operators twisted with almost flat bundles over V. Our perspective mainly comes from the asymptotic geometry of infinite groups and foliations.</div>
</front>
</TEI>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Istex/Curation
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 002B35 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Curation/biblio.hfd -nk 002B35 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Istex |étape= Curation |type= RBID |clé= ISTEX:D2681EB71F482A0EE9F8A12F1D8802C623FC24C6 |texte= Positive Curvature, Macroscopic Dimension, Spectral Gaps and Higher Signatures }}
This area was generated with Dilib version V0.6.33. |