Positive scalar curvature and strongly inessential manifolds

Alexander Dranishnikov

Positive scalar curvature and strongly inessential manifolds

Differential Geometry 2021-05-18 v1 Algebraic Topology General Topology

Authors: Alexander Dranishnikov

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 $u:M'\to K(\pi_1(M'),1)$ 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.

Keywords

positive scalar curvature strongly inessential manifolds closed n-manifolds abelian fundamental group finite covering classifying map

Cite

@article{arxiv.2105.07528,
  title  = {Positive scalar curvature and strongly inessential manifolds},
  author = {Alexander Dranishnikov},
  journal= {arXiv preprint arXiv:2105.07528},
  year   = {2021}
}

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