Higher index theory for spaces with an FCE-by-FCE structure

Jintao Deng; Liang Guo; Qin Wang; Guoliang Yu

paper

Higher index theory for spaces with an FCE-by-FCE structure

arXiv:2311.01665

Abstract

Let $(1 \to N_{n} \to G_{n} \to Q_{n} \to 1)_{n \in N}$ be a sequence of extensions of finite groups. Assume that the coarse disjoint unions of $(N_{n})_{n \in N}$ , $(G_{n})_{n \in N}$ and $(Q_{n})_{n \in N}$ have bounded geometry. The sequence $(G_{n})_{n \in N}$ is said to have an \emph{FCE-by-FCE structure}, if the sequence $(N_{n})_{n \in N}$ and the sequence $(Q_{n})_{n \in N}$ 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.