A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory
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- by G. C. Bell and A. N. Dranishnikov PDF
- Trans. Amer. Math. Soc. 358 (2006), 4749-4764 Request permission
Abstract:
We prove an asymptotic analog of the classical Hurewicz theorem on mappings that lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite-dimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension. As applications we find upper bound estimates for the asymptotic dimension of nilpotent and polycyclic groups in terms of their Hirsch length. We are also able to improve the known upper bounds on the asymptotic dimension of fundamental groups of complexes of groups, amalgamated free products and the hyperbolization of metric spaces possessing the Higson property.References
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Additional Information
- G. C. Bell
- Affiliation: Department of Mathematics, Penn State University, University Park, Pennsylvania 16802
- Address at time of publication: Mathematical Sciences, University of North Carolina at Greensboro, Greensboro, North Carolina 27402
- ORCID: 0000-0003-4297-0198
- Email: bell@math.psu.edu, gcbell@uncg.edu
- A. N. Dranishnikov
- Affiliation: Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, Florida 32611-8105
- MR Author ID: 212177
- Email: dranish@math.ufl.edu
- Received by editor(s): July 20, 2004
- Published electronically: April 17, 2006
- Additional Notes: The second author was partially supported by NSF Grant DMS-0305152
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 358 (2006), 4749-4764
- MSC (2000): Primary 20F69, 20F65; Secondary 20E08, 20E06
- DOI: https://doi.org/10.1090/S0002-9947-06-04088-8
- MathSciNet review: 2231870