Group approximation in Cayley topology and coarse geometry. II: Fibred coarse embeddings (Q2334942)

The paper follows from the first part [the authors, J. Topol. Anal. 13, No. 1, 1--47 (2021; Zbl 1479.20032)] and shows that a fibered coarse embedding (which is weaker than a coarse embedding) to a Hilbert space is equivalent to a uniformly a-T-menable at all limit points. More generally, it relates the possiblity of fibered coarse embeddings to more general Banach spaces with generalized versions of a-T-menability of the limit sets. It also provides examples showing that the change of marking in a set of finite groups can result in a very different coarse geometry.