More Extreme Limits of Manifolds with Positive Scalar Curvature

TL;DR

This paper constructs new examples of manifolds with positive scalar curvature that converge to limit spaces with infinitely many poles, providing tools to test different notions of weak scalar curvature.

Contribution

It extends previous constructions to produce new manifolds satisfying Gromov's conjecture assumptions, with limits featuring infinitely many poles in ^2.

Findings

Sequences converge to limit spaces with infinitely many poles

Examples can be used to test notions of weak scalar curvature

Builds on Sormani-Tian-Wang construction

Abstract

In this article, we extend the example constructed in the paper by Sormani-Tian-Wang to build new examples that satisfy the assumptions of the conjecture by Gromov. Each of these new examples of sequence converges to a limit space with infinitely many poles in $\mathbb{S}^2$. These examples can be used to test various notions of weak scalar curvature.