# Margulis lemma and Hurewicz fibration theorem on Alexandrov spaces

@article{Xu2019MargulisLA, title={Margulis lemma and Hurewicz fibration theorem on Alexandrov spaces}, author={Shicheng Xu and Xuchao Yao}, journal={Communications in Contemporary Mathematics}, year={2019} }

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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