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Structure of fundamental groups of manifolds with Ricci curvature bounded below
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abstract
Verifying a conjecture of Gromov we establish a generalized Margulis Lemma for manifolds with lower Ricci curvature bound. Among the various applications are finiteness results for fundamental groups of compact $n$-manifolds with upper diameter and lower Ricci curvature bound modulo nilpotent normal subgroups.
Forward citations
Cited by 3 Pith papers
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Nonnegative Ricci Curvature, Euclidean Volume Growth, and the Fundamental Groups of Open $4$-Manifolds
Open 4-manifolds with nonnegative Ricci curvature and Euclidean volume growth of the universal cover have finitely generated, virtually abelian fundamental groups.
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Nonnegative Ricci curvature and virtual abelianness in dimensions less than 12
Proves that nonnegative Ricci curvature manifolds with sublinear diameter growth in dimension n<12 have almost abelian fundamental groups via a bound n >= 4s(s-1)+k+1 on nilpotent subgroups of rank k and step s.
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A Large-Diameter Fundamental-Gap Lower Bound for Horoconvex Domains
Establishes a D^{-3} lower bound on the fundamental gap for large horoconvex domains in hyperbolic space, matching a prior upper bound.
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