Results 21 to 30 of about 4,893,677 (289)
Dynamic asymptotic dimension and Matui's HK conjecture [PDF]
Proceedings of the London Mathematical Society, 2021 We prove that the homology groups of a principal ample groupoid vanish in dimensions greater than the dynamic asymptotic dimension of the groupoid (as a side‐effect of our methods, we also give a new model of groupoid homology in terms of the Tor groups ...
Christian Bonicke +3 more
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A Hurewicz‐type theorem for the dynamic asymptotic dimension with applications to coarse geometry and dynamics [PDF]
Journal of the London Mathematical Society, 2022 We prove a Hurewicz‐type theorem for the dynamic asymptotic dimension originally introduced by Guentner, Willett, and Yu. Calculations of (or simply upper bounds on) this dimension are known to have implications related to cohomology of group actions and
Samantha Pilgrim
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Decay of scalar curvature on uniformly contractible manifolds with finite asymptotic dimension [PDF]
Communications on Pure and Applied Mathematics, 2021 Gromov proved a quadratic decay inequality of scalar curvature for a class of complete manifolds. In this paper, we prove that for any uniformly contractible manifold with finite asymptotic dimension, its scalar curvature decays to zero at a rate ...
Jin-Min Wang +2 more
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Polynomial growth and asymptotic dimension [PDF]
Israel Journal of Mathematics, 2021 Bonamy et al. [4] showed that graphs of polynomial growth have finite asymptotic dimension. We refine their result showing that a graph of polynomial growth strictly less than n ^ k +1 has asymptotic dimension at most k .
P. Papasoglu
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Borel asymptotic dimension and hyperfinite equivalence relations [PDF]
Duke mathematical journal, 2020 A long standing open problem in the theory of hyperfinite equivalence relations asks if the orbit equivalence relation generated by a Borel action of a countable amenable group is hyperfinite.
C. Conley +4 more
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Asymptotic Dimension of Minor-Closed Families and Assouad-Nagata Dimension of Surfaces [PDF]
Journal of the European Mathematical Society (Print), 2020 The asymptotic dimension is an invariant of metric spaces introduced by Gromov in the context of geometric group theory. In this paper, we study the asymptotic dimension of metric spaces generated by graphs and their shortest path metric and show their ...
Marthe Bonamy +6 more
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Universal derivation of the asymptotic charges of bosonic massless particles
Physics Letters B, 2023 We present a unified treatment of the conserved asymptotic charges associated with any bosonic massless particle in any spacetime dimension. In particular we provide master formulae for the asymptotic charges and the central extensions in the ...
Kevin Nguyen, Peter West
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Asymptotic dimension of discrete groups [PDF]
Fundamenta Mathematicae, 2006 We extend Gromov's notion of asymptotic dimension of finitely generated groups to all discrete groups. In particular, we extend the Hurewicz type theorem proven in [B-D2] to general groups. Then we use this extension to prove a formula for the asymptotic dimension of finitely generated solvable groups in terms of their Hirsch length.
Dranishnikov, A., Smith, J.
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On asymptotic Assouad–Nagata dimension
Topology and its Applications, 2007 28 pages, 0 ...
University of Florida, Department of Mathematics, PO Box 118105 Little Hall, Gainesville, FL 32611-8105, USA ( host institution ) +2 more
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Dynamic asymptotic dimension for actions of virtually cyclic groups [PDF]
Proceedings of the Edinburgh Mathematical Society, 2020 We show that the dynamic asymptotic dimension of an action of an infinite virtually cyclic group on a compact Hausdorff space is always one if the action has the marker property.
M. Amini +3 more
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