Let $(1\to N_n\to G_n\to Q_n\to 1)_{ n\in\mathbb{ N}}$ be a sequence of extensions of finite groups. Assume that the coarse disjoint unions of $(N_n)_{ n \in \mathbb{ N}}$, $(G_n)_{ n \in \mathbb{ N}}$ and $(Q_n)_{ n \in \mathbb{ N}}$ have bounded geometry. The sequence $(G_n)_{ n\in\mathbb{ N}}$ is said to have an \emph{ FCE-by-FCE structure}, if the sequence $(N_n)_{ n\in\mathbb{ N}}$ and the sequence $(Q_n)_{ n\in\mathbb{ N}}$ admit \emph{ a fibred coarse embedding} into Hilbert space. In this paper, we show that the coarse Novikov conjecture holds for spaces with an FCE-by-FCE structure.
Categories: math.KT math.FA math.OA