Open manifold with nonnegative Ricci curvature and collapsing volume

TL;DR

This paper investigates open manifolds with nonnegative Ricci curvature and collapsing volume, showing they have finite topological type under certain curvature bounds and restrictions.

Contribution

It establishes conditions under which open manifolds with nonnegative Ricci curvature and collapsing volume are of finite topological type.

Findings

Manifolds with nonnegative Ricci curvature and collapsing volume can have finite topological type.

Radial sectional curvature bounds influence the topological classification.

Specific restrictions ensure finiteness of topological type.

Abstract

In this paper, an n-dimensional complete open manifold with nonnegative Ricci curvature and collapsing volume has been investigated. If its radial sectional curvature bounded from below, it shows that such a manifold is of finite topological type under some restrictions shown below.