Positive scalar curvature for manifolds with elementary abelian fundamental group
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- by Boris Botvinnik and Jonathan Rosenberg PDF
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Abstract:
The statement often called the Gromov-Lawson-Rosenberg Conjecture asserts that a manifold with finite fundamental group should admit a metric of positive scalar curvature except when the $KO_*$-valued index of some Dirac operator with coefficients in a flat bundle is non-zero. We prove spin and oriented non-spin versions of this statement for manifolds (of dimension $\ge 5$) with elementary abelian fundamental groups $\pi$, except for “toral” classes, and thus our results are automatically applicable once the dimension of the manifold exceeds the rank of $\pi$. The proofs involve the detailed structure of $BP_*(B\pi )$, as computed by Johnson and Wilson.References
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Additional Information
- Boris Botvinnik
- Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222
- MR Author ID: 235944
- Email: botvinn@poincare.uoregon.edu
- Jonathan Rosenberg
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015
- MR Author ID: 298722
- ORCID: 0000-0002-1531-6572
- Email: jmr@math.umd.edu
- Received by editor(s): June 21, 2002
- Published electronically: September 16, 2004
- Additional Notes: We thank Sergey Novikov for helping to make this collaboration possible
This work was partially supported by NSF grant DMS-0103647 - Communicated by: Wolfgang Ziller
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 545-556
- MSC (2000): Primary 53C20; Secondary 53C21, 55S30, 55N22, 55U25, 57R75
- DOI: https://doi.org/10.1090/S0002-9939-04-07762-7
- MathSciNet review: 2093079