Topological finiteness for asymptotically nonnegatively curved manifolds

TL;DR

This paper proves that certain asymptotically nonnegatively curved manifolds with Euclidean volume growth have finitely many topological types, advancing understanding of their geometric and topological classification.

Contribution

It establishes topological finiteness for a class of asymptotically nonnegatively curved manifolds under volume growth conditions, extending previous results in geometric topology.

Findings

Finiteness of homeomorphism types for the class considered

Volume growth conditions imply topological restrictions

Extension of topological classification in nonnegative curvature settings

Abstract

We prove that a class of asymptotically nonnegatively curved manifolds (in the sense of Abresch) satisfying some uniform Euclidean type volume growth conditions contains only finitely many homeomorphism types.