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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymptotic properties of groups acting on complexes


Author: Gregory C. Bell
Journal: Proc. Amer. Math. Soc. 133 (2005), 387-396
MSC (2000): Primary 20F69; Secondary 20E08, 20E06
Published electronically: September 8, 2004
MathSciNet review: 2093059
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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: http://dx.doi.org/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
Published electronically: September 8, 2004
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.