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

DOI:
https://doi.org/10.1090/S0002-9939-04-07630-0

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:
https://doi.org/10.1090/S0002-9939-04-07630-0

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.