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Register a new userPositive scalar curvature and strongly inessential manifolds
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Alexander Dranishnikov
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We prove that a closed $n$-manifold $M$ with positive scalar curvature and abelian fundamental group admits a finite covering $M$ which is strongly inessential. The latter means that a classifying map $u:Mto K(pi_1(M),1)$ can be deformed to the $(n-2)$-skeleton. This is proven for all $n$-manifolds with the exception of 4-manifolds with spin universal coverings.
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