Examples of manifolds of positive Ricci curvature with quadratically nonnegatively curved infinity and infinite topological type

TL;DR

This paper constructs specific high-dimensional manifolds with positive Ricci curvature and quadratic nonnegative curvature at infinity, providing counterexamples to a conjecture in differential geometry.

Contribution

It introduces new examples of manifolds with positive Ricci curvature and infinite topological type, challenging previous conjectures in the field.

Findings

Constructed manifolds with positive Ricci curvature and quadratic nonnegative curvature at infinity

Provided counterexamples to a conjecture by Sha and Shen for dimensions ≥ 6

Demonstrated existence of manifolds with infinite topological complexity

Abstract

In this paper, we construct a complete n-dim Riemannian manifold with positive Ricci curvature, quadratically nonnegatively curved infinity and infinite topological type. This gives a negative answer to a conjecture by Jiping Sha and Zhongmin Shen in the case of n greater than or equal to 6.