Year: 2025
Type: article
Abstract: We prove some finiteness results for discrete isometry groups $$\Gamma $$ Γ of uniformly packed CAT(0)-spaces X with uniformly bounded codiameter (up to group isomorphism), and for CAT(0)-orbispaces $$M = \Gamma \backslash X$$ M = Γ \ X (up to equivariant homotopy equivalence or equivariant diffeomorphism); these results generalize, in nonpositive curvature, classical finiteness theorems of Riemannian geometry. As a corollary, the order of every torsion subgroup of $$\Gamma $$ Γ is bounded above by a universal constant only depending on the packing constants and the codiameter. The main tool is a splitting theorem for sufficiently collapsed actions: namely we show that if a geodesically complete, packed, CAT(0)-space admits a discrete, cocompact group of isometries with sufficiently small systole then it necessarily splits a non-trivial Euclidean factor.
Source: Mathematische Annalen
Authors: Nicola Cavallucci, Andrea Sambusetti
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Award: G470993797
OpenAlex ID: W4409623210