Fukaya-Yamaguchi Conjecture in Dimension Four (Journal of Mathematical Study, 2025)
Fukaya and Yamaguchi conjectured that if $M^n$ is a manifold with nonnegative sectional curvature, then the fundamental group is uniformly virtually abelian. In this short note we observe that the conjecture holds in dimensions up to four.
Keywords: Sectional curvature; fundamental group; abelian