Zobrazeno 1 - 10
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pro vyhledávání: '"Higes, J."'
We prove that the asymptotic Assouad-Nagata dimension of a connected Lie group $G$ equipped with a left-invariant Riemannian metric coincides with its topological dimension of $G/C$ where $C$ is a maximal compact subgroup. To prove it we will compute
Externí odkaz:
http://arxiv.org/abs/0910.4569
Autor:
Brodskiy, N., Higes, J.
Given a metric space $X$ of finite asymptotic dimension, we consider a quasi-isometric invariant of the space called dimension function. The space is said to have asymptotic Assouad-Nagata dimension less or equal $n$ if there is a linear dimension fu
Externí odkaz:
http://arxiv.org/abs/0910.2378
Autor:
Higes, J., Mitrra, A.
In this note we prove that every metric space $(X, d)$ of asymptotic dimmension at most $n$ is coarsely equivalent to a metric space $(Y, D)$ that satisfies the following property of Nagata: For every $n+2$ points $y_1,..., y_{n+2}$ in $Y$ and for ev
Externí odkaz:
http://arxiv.org/abs/0812.1641
We prove that two countable locally finite-by-abelian groups G,H endowed with proper left-invariant metrics are coarsely equivalent if and only if their asymptotic dimensions coincide and the groups are either both finitely-generated or both are infi
Externí odkaz:
http://arxiv.org/abs/0807.1141
Autor:
Higes, J.
Suppose $G$ is a countable, not necessarily finitely generated, group. We show $G$ admits a proper, left-invariant metric $d_G$ such that the Assouad-Nagata dimension of $(G,d_G)$ is infinite, provided the center of $G$ is not locally finite. As a co
Externí odkaz:
http://arxiv.org/abs/0804.4533
Autor:
Higes, J.
We classify up to coarse equivalence all countable abelian groups of finite torsion free rank. The Q-cohomological dimension and the torsion free rank are the two invariants that give us such classification. We also prove that any countable abelian g
Externí odkaz:
http://arxiv.org/abs/0803.0379
Autor:
Higes, J.
In this work we study two problems about Assouad-Nagata dimension: 1) Is there a metric space of non zero Assouad-Nagata dimension such that all of its asymptotic cones are of Assouad-Nagata dimension zero? (Dydak and Higes) 2) Suppose $G$ is a local
Externí odkaz:
http://arxiv.org/abs/0711.1512
Publikováno v:
Proceedings of the American Math.Soc. 136 (2008), 2225--2233
We prove the dimension of any asymptotic cone over a metric space X does not exceed the asymptotic Assouad-Nagata dimension of X. This improves a result of Dranishnikov and Smith who showed that dim(Y) does not exceed asymptotic Assouad-Nagata dimens
Externí odkaz:
http://arxiv.org/abs/math/0610338
Autor:
Higes, J.
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. There are also semigroup controlled dimensions for the small scale an
Externí odkaz:
http://arxiv.org/abs/math/0608736
Publikováno v:
Topology and its Applications, 154 (2007), 2729-2740
We consider the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the category of (unbounded) separable metric spaces and (metrically proper) uniform maps. A unifie
Externí odkaz:
http://arxiv.org/abs/math/0607241