Assouad-Nagata dimension of connected Lie groups
SCIE
SCOPUS
- Title
- Assouad-Nagata dimension of connected Lie groups
- Authors
- Higes, J; Peng, I
- Date Issued
- 2013-02
- Publisher
- Springer
- Abstract
- 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 the Assouad-Nagata dimension of connected solvable Lie groups and semisimple Lie groups. As a consequence we show that the asymptotic Assouad-Nagata dimension of a polycyclic group equipped with a word metric is equal to its Hirsch length and that some wreath-type finitely generated groups can not be quasi-isometrically embedded into any cocompact lattice on a connected Lie group.
- Keywords
- Asymptotic dimension; Assouad-Nagata dimension; Polycyclic groups; Connected Lie groups; ASYMPTOTIC DIMENSION; DISCRETE-GROUPS; LIPSCHITZ EXTENSIONS; UNIFORM EMBEDDINGS; SPACES; CONES
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/15673
- DOI
- 10.1007/S00209-012-1004-1
- ISSN
- 0025-5874
- Article Type
- Article
- Citation
- Mathematische Zeitschrift, vol. 273, no. 1-2, page. 283 - 302, 2013-02
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