Structure of Fundamental Groups of Manifolds with Ricci Curvature Bounded Below

@inproceedings{WILKING2011StructureOF,
  title={Structure of Fundamental Groups of Manifolds with Ricci Curvature Bounded Below},
  author={BURKHARD WILKING},
  year={2011}
}
  • BURKHARD WILKING
  • Published 2011
We call a generator system b1, . . . , bn of a group N a nilpotent basis if the commutator [bi, bj ] is contained in the subgroup 〈b1, . . . , bi−1〉 for 1 ≤ i < j ≤ n. Having a nilpotent basis of length n implies in particular rank(N) ≤ n. We will also show that equality in this inequality can only occur if M is homeomorphic to an infranilmanifold, see Corollary 7.1. In the case of a sectional curvature bound the theorem is due to Kapovitch, Petrunin and Tuschmann [KPT10], based on an earlier… CONTINUE READING

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