Margulis lemma and Hurewicz fibration theorem on Alexandrov spaces

  title={Margulis lemma and Hurewicz fibration theorem on Alexandrov spaces},
  author={Shicheng Xu and Xuchao Yao},
  journal={Communications in Contemporary Mathematics},
1 We prove the generalized Margulis lemma with a uniform index bound on an Alexandrov [Formula: see text]-space [Formula: see text] with curvature bounded below, i.e. small loops at [Formula: see text] generate a subgroup of the fundamental group of the unit ball [Formula: see text] that contains a nilpotent subgroup of index [Formula: see text], where [Formula: see text] is a constant depending only on the dimension [Formula: see text]. The proof is based on the main ideas of V. Kapovitch, A… 


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  • Linan Chen
  • Computer Science
    Proceedings of the American Mathematical Society
  • 2022
It is shown that the quantitative maximal volume entropy rigidity holds on Alexandrov spaces, given inline-formula content-type math/mathml.



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