Circle bundles with PSC over large manifolds

2024/12/02 by Aditya Kumar, Kumar, Aditya, Balarka Sen +1 · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2412.01047

Abstract

We construct infinitely many examples of macroscopically large manifolds of dimension m ≥ 4 equipped with circle bundles whose total spaces admit metrics of positive scalar curvature and have macroscopic dimension at most \lceil m/2 \rceil + 1. In particular, we answer a question of Gromov on the existence of circle bundles over enlargeable manifolds whose total spaces admit metrics of positive scalar curvature, in all dimensions. Our constructions are based on techniques from symplectic geometry.

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• Scalar Curvature in Dimension 4

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