The coarse Novikov conjecture for extensions of coarsely embeddable groups

Abstract

Let (1 → Nn → Gn → Qn → 1) n∈N be a sequence of extensions of countable discrete groups.Endow (Gn) n∈N with metrics associated to proper length functions on (Gn) n∈N respectively such that the sequence of metric spaces (Gn) n∈N have uniform bounded geometry. We show that if (Nn) n∈N and (Qn) n∈N are coarsely embeddable into Hilbert space, then the coarse Novikov conjecture holds for the sequence (Gn) n∈N , which may not admit a coarse embedding into Hilbert space.