Thin actions on CAT(0) spaces

2022/10/03 by Cavallucci, Nicola, Sambusetti, Andrea
#53C21 #53C23 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2210.01085

Abstract

We study groups of isometries of packed, geodesically complete, CAT(0)-spaces for which the systole at every point is smaller than a universal constant depending only on the packing, deducing strong rigidity results. We show that if a space as above has some negative curvature behaviour then it cannot support a thin action: this generalizes the classical Margulis Lemma to a broader class of spaces.

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