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Assouad-Nagata dimension of nilpotent groups with arbitrary left invariant metrics
Author(s):
J.
Higes
Journal:
Proc. Amer. Math. Soc.
138
(2010),
2235-2244.
MSC (2000):
Primary 54F45;
Secondary 55M10, 54C65
Posted:
February 12, 2010
MathSciNet review:
2596064
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Abstract:
Suppose  is a countable, not necessarily finitely generated, group. We show  admits a proper, left invariant metric  such that the Assouad-Nagata dimension of  is infinite, provided the center of  is not locally finite. As a corollary we solve two problems of A. Dranishnikov.
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Additional Information:
J.
Higes
Affiliation:
Departamento de Geometría y Topología, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid, 28040, Spain
Email:
josemhiges@yahoo.es
DOI:
10.1090/S0002-9939-10-10240-8
PII:
S 0002-9939(10)10240-8
Keywords:
Assouad-Nagata dimension,
asymptotic dimension,
nilpotent groups
Received by editor(s):
June 11, 2009,
Received by editor(s) in revised form:
October 3, 2009
Posted:
February 12, 2010
Additional Notes:
The author is supported by Grant AP2004-2494 from the Ministerio de Educación y Ciencia, Spain, and project MEC, MTM2006-0825. He also thanks Jerzy Dydak and N. Brodskyi for helpful comments and support.
Communicated by:
Alexander N. Dranishnikov
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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