Fundamental Groups of Spaces with Bakry-Emery Ricci Tensor Bounded Below

2013/09/25 by Maree Jaramillo, Jaramillo, Maree
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1309.6685

openalex publication_date 2013/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first extend Cheeger-Colding Almost Splitting Theorem to smooth metric measure spaces. Arguments utilizing this extension of the Almost Splitting Theorem show that if a smooth metric measure space has almost nonnegative Bakry-Emery Ricci curvature and a lower bound on volume, then its fundamental group is almost abelian. Second, if the smooth metric measure space has Bakry-Emery Ricci curvature bounded from below then the number of generators of the fundamental group is uniformly bounded. These results are extensions of theorems which hold for Riemannian manifolds with Ricci curvature bounded from below.

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