# Manifolds of positive Ricci curvature, quadratically asymptotically nonnegative curvature, and infnite Betti numbers

## TL;DR

This paper constructs new examples of high-dimensional complete manifolds with positive Ricci curvature, quadratic asymptotic nonnegativity, and infinite Betti numbers, expanding understanding of their topological and geometric properties.

## Contribution

It introduces a novel method to produce high-dimensional manifolds with positive Ricci curvature and specific topological features, including infinite Betti numbers.

## Key findings

- Constructed families of manifolds with positive Ricci curvature and infinite Betti numbers.
- Demonstrated quadratic asymptotic nonnegativity of sectional curvature in these manifolds.
- Extended previous work to include manifolds of dimension at least 5.

## Abstract

In a previous paper, we constructed complete manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type but dimension $\ge 6$. The purpose of the present paper is to use a different way to exhibit a family of complete $I$-dimensinal ($I\ge5$) Riemannian manifolds of positive Ricci curvature, quadratically asymptotically nonnegative sectional curvature, and certain infinite Betti number $b_j$ ($2\le j\le I-2$).