A transformation theorem is proved under a non-decreasing monotonicity condition on almost-Euclidean factors, yielding finite generation and virtual abelianness of fundamental groups for certain nonnegatively Ricci-curved manifolds.
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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.
Slow relative volume growth on complete manifolds with nonnegative Ricci curvature implies almost abelian or finite fundamental groups.
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Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls
A transformation theorem is proved under a non-decreasing monotonicity condition on almost-Euclidean factors, yielding finite generation and virtual abelianness of fundamental groups for certain nonnegatively Ricci-curved manifolds.
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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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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.