Year: 2018
Type: preprint
Abstract: We define two different weakenings of coarse amenability (also known as Yu's property A), namely fibred coarse amenability and coarse amenability at infinity. These two properties allow us to prove that a residually finite group is coarsely amenable if and only if some (or all) of its box spaces satisfy the weak properties. We then elaborate on a result of Willett by showing that graphs with large girth always satisfy fibred coarse amenability. Finally, we discuss some examples and counter-examples to these properties.
Source: arXiv (Cornell University)
Author: Pillon, Thibault
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2907527893