Geodesic
On asymptotic dimension of groups
Bell, G1 ; Dranishnikov, Alexander N1
1University of Florida, Department of Mathematics, PO Box 118105, 358 Little Hall, Gainesville FL 32611-8105, USA
Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 57-71
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We prove a version of the countable union theorem for asymptotic dimension and we apply it to groups acting on asymptotically finite dimensional metric spaces. As a consequence we obtain the following finite dimensionality theorems.

A) An amalgamated product of asymptotically finite dimensional groups has finite asymptotic dimension: asdimA ∗CB < ∞.

B) Suppose that G′ is an HNN extension of a group G with asdimG < ∞. Then asdimG′ < ∞.

C) Suppose that Γ is Davis’ group constructed from a group π with asdimπ < ∞. Then asdimΓ < ∞.

DOI : 10.2140/agt.2001.1.57
Keywords: Asymptotic dimension, amalgamated product, HNN extension

Bell, G  1   ; Dranishnikov, Alexander N  1

1 University of Florida, Department of Mathematics, PO Box 118105, 358 Little Hall, Gainesville FL 32611-8105, USA 
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Bell, G; Dranishnikov, Alexander N. On asymptotic dimension of groups. Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 57-71. doi: 10.2140/agt.2001.1.57

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