Positive Curvature, Macroscopic Dimension, Spectral Gaps and Higher Signatures
Identifieur interne : 000552 ( France/Analysis ); précédent : 000551; suivant : 000553Positive 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
Affiliations:
- France, États-Unis
- Maryland, Île-de-France
- Bures-sur-Yvette, College Park (Maryland)
- Université du Maryland
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ISTEX:D2681EB71F482A0EE9F8A12F1D8802C623FC24C6Le document en format XML
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