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2018 On the stability of asymptotic property C for products and some group extensions
Gregory Copeland Bell, Andrzej Nagórko
Algebr. Geom. Topol. 18(1): 221-245 (2018). DOI: 10.2140/agt.2018.18.221

Abstract

We show that Dranishnikov’s asymptotic property C is preserved by direct products and the free product of discrete metric spaces. In particular, if G and H are groups with asymptotic property C, then both G × H and G H have asymptotic property C. We also prove that a group  G has asymptotic property C if 1 K G H 1 is exact, asdim K < and H has asymptotic property C. The groups are assumed to have left-invariant proper metrics and need not be finitely generated. These results settle questions of Dydak and Virk (2016), of Bell and Moran (2015) and an open problem in topology.

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Gregory Copeland Bell. Andrzej Nagórko. "On the stability of asymptotic property C for products and some group extensions." Algebr. Geom. Topol. 18 (1) 221 - 245, 2018. https://doi.org/10.2140/agt.2018.18.221

Information

Received: 22 July 2016; Revised: 29 June 2017; Accepted: 21 July 2017; Published: 2018
First available in Project Euclid: 1 February 2018

zbMATH: 06828004
MathSciNet: MR3748243
Digital Object Identifier: 10.2140/agt.2018.18.221

Subjects:
Primary: 54F45
Secondary: 20F69

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 1 • 2018
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