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Asymptotic properties of groups acting on complexes
Author(s):
Gregory
C.
Bell
Journal:
Proc. Amer. Math. Soc.
133
(2005),
387-396.
MSC (2000):
Primary 20F69;
Secondary 20E08, 20E06
Posted:
September 8, 2004
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Abstract:
We examine asymptotic dimension and property A for groups acting on complexes. In particular, we prove that the fundamental group of a finite, developable complex of groups will have finite asymptotic dimension provided the geometric realization of the development has finite asymptotic dimension and the vertex groups are finitely generated and have finite asymptotic dimension. We also prove that property A is preserved by this construction provided the geometric realization of the development has finite asymptotic dimension and the vertex groups all have property A. These results naturally extend the corresponding results on preservation of these large-scale properties for fundamental groups of graphs of groups. We also use an example to show that the requirement that the development have finite asymptotic dimension cannot be relaxed.
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Additional Information:
Gregory
C.
Bell
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Email:
bell@math.psu.edu
DOI:
10.1090/S0002-9939-04-07630-0
PII:
S 0002-9939(04)07630-0
Keywords:
Complexes of groups,
asymptotic dimension,
property A
Received by editor(s):
December 5, 2002
Received by editor(s) in revised form:
September 23, 2003
Posted:
September 8, 2004
Communicated by:
Stephen D. Smith
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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