On Gromov's scalar curvature conjecture

We prove the Gromov conjecture on the macroscopic dimension of the universal covering of a closed spin manifold with a positive scalar curvature under the following assumptions on the fundamental group: 1. The Strong Novikov Conjecture holds for \(\pi\). 2. The natural map \(per:ko_n(B\pi)\to KO_n(B...

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Bibliographic Details
Published inarXiv.org
Main Authors Bolotov, Dmitry, Dranishnikov, Alexander
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.01.2009
Subjects
Curvature
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Summary:We prove the Gromov conjecture on the macroscopic dimension of the universal covering of a closed spin manifold with a positive scalar curvature under the following assumptions on the fundamental group: 1. The Strong Novikov Conjecture holds for \(\pi\). 2. The natural map \(per:ko_n(B\pi)\to KO_n(B\pi)\) is injective.
ISSN:2331-8422