Positive scalar curvature metrics and aspherical summands

2023/12/07 by Chen, Shuli, Chu, Jianchun, Zhu, Jintian · 3 citations
#53A10 #53C21 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2312.04698

Abstract

We prove for n∈\3,4,5\ that the connected sum of a closed aspherical n-manifold with an arbitrary non-compact manifold does not admit a complete metric with nonnegative scalar curvature. In particular, a special case of our result answers a question of Gromov. More generally, we generalize the partial classification result of Chodosh, Li, and Liokumovich to the non-compact domination case with our newly-developed technique. Our result unifies all previous results of this type, and confirms the validity of Gromov's non-compact domination conjecture for closed aspherical manifolds of dimensions 3, 4, and 5.

Cited by

• Non-negative scalar curvature on spin surgeries and Novikov conjecture
• Minimal surfaces and comparison geometry
• Optimal decay constant for complete manifolds of positive scalar curvature with quadratic decay

Related

• Positive scalar curvature and connected sums
• Positive Scalar Curvature on Noncompact Manifolds and the Liouville Theorem
• Generalized soap bubbles and the topology of manifolds with positive scalar curvature
• Interior control for surfaces with positive scalar curvature and its application
• Connected sum constructions for constant scalar curvature metrics