Results 11 to 20 of about 4,893,677 (289)
Complexity of finite Borel asymptotic dimension [PDF]
Forum of Mathematics, SigmaWe show that the set of locally finite Borel graphs with finite Borel asymptotic dimension is $\boldsymbol {\Sigma }^1_2$ -complete. The result is based on a combinatorial characterization of finite Borel asymptotic dimension for graphs generated ...
Jan Grebík, Cecelia Higgins
doaj +4 more sources
Hyperfiniteness and Borel asymptotic dimension of boundary actions of hyperbolic groups. [PDF]
Math Ann, 2023 We give a new short proof of the theorem due to Marquis and Sabok, which states that the orbit equivalence relation induced by the action of a finitely generated hyperbolic group on its Gromov boundary is hyperfinite.
Naryshkin P, Vaccaro A.
europepmc +3 more sources
Asymptotic dimension of intersection graphs [PDF]
European Journal of Combinatorics, 2022 We show that intersection graphs of compact convex sets in R^n of bounded aspect ratio have asymptotic dimension at most 2n+1. More generally, we show this is the case for intersection graphs of systems of subsets of any metric space of Assouad-Nagata ...
Zdeněk Dvořák, S. Norin
semanticscholar +5 more sources
On the dynamic asymptotic dimension of étale groupoids [PDF]
Mathematische Zeitschrift, 2023 We investigate the dynamic asymptotic dimension for étale groupoids introduced by Guentner, Willett and Yu. In particular, we establish several permanence properties, including estimates for products and unions of groupoids.
Christian Bonicke
semanticscholar +5 more sources
Topological rigidity of the dynamic asymptotic dimension [PDF]
Groups, Geometry, and Dynamics, 2023 We show for a free action of a countable group \Gamma on a finite-dimensional, compact metric space by homeomorphisms that the dynamic asymptotic dimension is either infinite or coincides with the asymptotic dimension of \Gamma .
Samantha Pilgrim
semanticscholar +3 more sources
Asymptotic dimension and the disk graph I: ASYMPTOTIC DIMENSION AND DISK GRAPHS I [PDF]
Journal of Topology, 2019 We show that the asymptotic dimension of a hyperbolic relatively hyperbolic graph is finite, provided that this holds true uniformly for the peripheral subgraphs and for the electrification.
U. Hamenstädt
semanticscholar +9 more sources
Asymptotic dimension of fuzzy metric spaces [PDF]
Fuzzy Sets and Systems, 2020 In this paper, we define asymptotic dimension of fuzzy metric spaces in the sense of George and Veeramini. We prove that asymptotic dimension is an invariant in the coarse category of fuzzy metric spaces.
Pawel Grzegrzolka
semanticscholar +5 more sources
A Metric Space With Its Transfinite Asymptotic Dimension ω + 1
Topology and Its Applications, 2020 We construct a metric space whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both ω + 1 , where ω is the smallest infinite ordinal number. Therefore, we prove that the omega conjecture is not true.
Jingming Zhu
exaly +2 more sources
Asymptotic Charges at Null Infinity in Any Dimension
Universe, 2018 We analyse the conservation laws associated with large gauge transformations of massless fields in Minkowski space. Our aim is to highlight the interplay between boundary conditions and finiteness of the asymptotically conserved charges in any space-time
Andrea Campoleoni +2 more
doaj +3 more sources
Nuclear Dimension of Subhomogeneous Twisted Groupoid C*-algebras and Dynamic Asymptotic Dimension [PDF]
International mathematics research notices, 2023 We characterize subhomogeneity for twisted étale groupoid $\text{C}^{*}$-algebras and obtain an upper bound on their nuclear dimension. As an application, we remove the principality assumption in recent results on upper bounds on the nuclear dimension ...
Christian Bonicke, Kang Li
semanticscholar +1 more source