Rigidity result classifies torus bundles with affine structure groups under b1(M) - b1(N) = dim M - dim N, with splitting conditions for principal torus bundles.
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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.
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math.DG 4years
2026 4verdicts
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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.
Establishes a D^{-3} lower bound on the fundamental gap for large horoconvex domains in hyperbolic space, matching a prior upper bound.
Slow relative volume growth on complete manifolds with nonnegative Ricci curvature implies almost abelian or finite fundamental groups.
citing papers explorer
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Structure of Torus Fibration Under the First Betti Number Restriction
Rigidity result classifies torus bundles with affine structure groups under b1(M) - b1(N) = dim M - dim N, with splitting conditions for principal torus bundles.
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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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Complete manifolds with nonnegative Ricci curvature and slow relative volume growth
Slow relative volume growth on complete manifolds with nonnegative Ricci curvature implies almost abelian or finite fundamental groups.