Positive scalar curvature and strongly inessential manifolds

2021/05/16 by Dranishnikov, Alexander
#Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2105.07528

Abstract

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:M'→ K(π₁(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.

Related

• Positive scalar curvature -- constructions and obstructions
• Fundamental Group of Self-Dual Four-Manifolds with Positive Scalar\n Curvature
• Dissolving four-manifolds and positive scalar curvature
• A smooth variation of Baas-Sullivan Theory and Positive Scalar Curvature
• Highly connected manifolds of positive p-curvature