Geodesic
On the stability of asymptotic property C for products and some group extensions
Bell, Gregory1 ; Nagórko, Andrzej2
1 Department of Mathematics and Statistics, The University of North Carolina, Greensboro, NC, United States
2 Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Warszawa, Poland
Algebraic and Geometric Topology, Tome 18 (2018) no. 1, pp. 221-245

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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, asdimK < ∞ 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.

DOI : 10.2140/agt.2018.18.221
Classification : 54F45, 20F69
Keywords: asymptotic property C, asymptotic dimension, coarse geometry

Bell, Gregory 1 ; Nagórko, Andrzej 2

1 Department of Mathematics and Statistics, The University of North Carolina, Greensboro, NC, United States
2 Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Warszawa, Poland 
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Bell, Gregory; Nagórko, Andrzej. On the stability of asymptotic property C for products and some group extensions. Algebraic and Geometric Topology, Tome 18 (2018) no. 1, pp. 221-245. doi: 10.2140/agt.2018.18.221

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