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.
Thin actions on CAT(0) spaces / Cavallucci, Nicola; Sambusetti, Andrea. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 2036-2145. - (2024). [10.2422/2036-2145.202301_006]
Thin actions on CAT(0) spaces
Nicola Cavallucci
;Sambusetti
2024
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.File allegati a questo prodotto
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