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Mathematics > Metric Geometry

arXiv:2210.01085 (math)
[Submitted on 3 Oct 2022 (v1), last revised 28 Nov 2022 (this version, v3)]

Title:Thin actions on CAT(0) spaces

Authors:Nicola Cavallucci, Andrea Sambusetti
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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.
Comments: v2: Correction of minor errors in Step 3 of the proof of Theorem 3.1. Remark 3.4 accordingly updated v3: Affiliations added
Subjects: Metric Geometry (math.MG)
MSC classes: 53C21, 53C23
Cite as: arXiv:2210.01085 [math.MG]
  (or arXiv:2210.01085v3 [math.MG] for this version)
  https://doi.org/10.48550/arXiv.2210.01085

Submission history

From: Nicola Cavallucci [view email]
[v1] Mon, 3 Oct 2022 17:02:30 UTC (54 KB)
[v2] Thu, 13 Oct 2022 14:30:31 UTC (55 KB)
[v3] Mon, 28 Nov 2022 08:08:44 UTC (55 KB)
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