Asymptotic Dimension
By Gregory C. Bell, Alexander Dranishnikov. 2007
207 citations recorded by the source corpus.
. The asymptotic dimension theory was founded by Gromov [61] in the early 90s. In this paper we give a survey of its recent history where we emphasize two of its features: an analogy with the dimension theory of compact metric spaces and applications to the theory of discrete groups.
View Paper: https://www.semanticscholar.org/paper/8cf03cee4ac41b0d9c1f4c78a5aee2b77c33599a
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Citations in the corpus
- Dynamic asymptotic dimension: relation to dynamics, topology, coarse geometry, and $$C^*$$C∗-algebras (2015, background): “On the other hand, part (iv) implies that many interesting classes of groups—for example, word hyperbolic groups [32], CAT(0) cubical groups [43], lattices in Lie groups, and many solvable groups [4]—admit at least some actions with finite dynamic asymptotic dimension.”
- Dimension, comparison, and almost finiteness (2017, background): “See [1] for a general reference on the subject.”
- Borel asymptotic dimension and hyperfinite equivalence relations (2020, background): “68 in [2] and the remark following it).”
- The nuclear dimension of C*-algebras (2009, unknown): “ximations in (6), there is ¯ν∈ Nsuch that kσ(i) ¯λ,l, ¯ν (i) ¯λ,l, ¯ν(gζ,2ζ(ϕ (i) ¯λ,l (e 11))) −gζ,2ζ(ϕ (i) ¯λ,l (e ))k <ζ for each i∈ {0,...,n} and l∈ {1,...,r(i) ¯λ }. Here, we define gζ,2ζ ∈ C([0,1]) by gζ,2ζ(t) := 0 for 0 ≤ t≤ ζ, 1 for t≥ 2ζ, linear else. We then have X l ¯σ(i) λ,l,¯ ν¯ (1”
- Constructing group actions on quasi-trees and applications to mapping class groups (2010, methodology): “ x ∈ Xα\ YR and y∈ Xβ\ YR). Then asdim(X) ≤ n. Furthermore the uniformity constants for asdim(X) only depend on the uniformity constants for Xα and YR. Remark 4.22. The uniformity statement is not in [BD08] but is easily seen from the proof. We noted above that asymptotic dimension is not only a qua”