On Gromov’s scalar curvature conjecture
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- by Dmitry Bolotov and Alexander Dranishnikov PDF
- Proc. Amer. Math. Soc. 138 (2010), 1517-1524 Request permission
Abstract:
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.
$0.1$. Theorem. Suppose that a discrete group $\pi$ has the following properties:
$1$. The Strong Novikov Conjecture holds for $\pi$.
$2$. The natural map $per:ko_n(B\pi )\to KO_n(B\pi )$ is injective. Then the Gromov Macroscopic Dimension Conjecture holds true for spin $n$-manifolds $M$ with the fundamental groups $\pi _1(M)$ that contain $\pi$ as a finite index subgroup.
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Additional Information
- Dmitry Bolotov
- Affiliation: Verkin Institute of Low Temperature Physics, Lenina Avenue, 47, Kharkov, 631103, Ukraine
- Email: bolotov@univer.kharkov.ua
- Alexander Dranishnikov
- Affiliation: Department of Mathematics, 358 Little Hall, University of Florida, Gainesville, Florida 32611-8105
- MR Author ID: 212177
- Email: dranish@math.ufl.edu
- Received by editor(s): January 28, 2009
- Received by editor(s) in revised form: September 11, 2009
- Published electronically: December 8, 2009
- Additional Notes: This work was supported by NSF grant DMS-0604494
- Communicated by: Brooke Shipley
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1517-1524
- MSC (2010): Primary 55M30; Secondary 53C23, 57N65, 55N15
- DOI: https://doi.org/10.1090/S0002-9939-09-10199-5
- MathSciNet review: 2578547