Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Positive scalar curvature for manifolds with elementary abelian fundamental group

Author(s): Boris Botvinnik; Jonathan Rosenberg
Journal: Proc. Amer. Math. Soc. 133 (2005), 545-556.
MSC (2000): Primary 53C20; Secondary 53C21, 55S30, 55N22, 55U25, 57R75
Posted: September 16, 2004
MathSciNet review: 2093079
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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 -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 $\ge5$ ) 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.

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