Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Gromov's scalar curvature conjecture


Authors: Dmitry Bolotov and Alexander Dranishnikov
Journal: Proc. Amer. Math. Soc. 138 (2010), 1517-1524
MSC (2010): Primary 55M30; Secondary 53C23, 57N65, 55N15
Published electronically: December 8, 2009
MathSciNet review: 2578547
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 55M30, 53C23, 57N65, 55N15

Retrieve articles in all journals with MSC (2010): 55M30, 53C23, 57N65, 55N15


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
Email: dranish@math.ufl.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10199-5
PII: S 0002-9939(09)10199-5
Keywords: Positive scalar curvature, macroscopic dimension, connective $K$-theory, Strong Novikov Conjecture
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.