5 citations · 7 across the 5 of their papers we have counts for
5 papers
Assouad-Nagata dimension of tree-graded spaces
N. Brodskiy, J. Higes
Given a metric space of finite asymptotic dimension, we consider a quasi-isometric invariant of the space called dimension function. The space is said to have asymptotic Assoua…
Assouad-Nagata dimension of connected Lie groups
J. Higes, I. Peng
We prove that the asymptotic Assouad-Nagata dimension of a connected Lie group equipped with a left-invariant Riemannian metric coincides with its topological dimension of $G/C…
On asymptotic dimension and a property of Nagata
J. Higes, A. Mitrra
In this note we prove that every metric space of asymptotic dimmension at most is coarsely equivalent to a metric space that satisfies the following property…
Assuad-Nagata dimension of nilpotent groups with arbitrary left invariant metrics
J. Higes
Suppose is a countable, not necessarily finitely generated, group. We show admits a proper, left-invariant metric such that the Assouad-Nagata dimension of …
Semigroup-controlled asymptotic dimension
J. Higes
We introduce the idea of semigroup-controlled asymptotic dimension. This notion generalizes the asymptotic dimension and the asymptotic Assouad-Nagata dimension in the large scale.…