The Coarse Novikov Conjecture for Finite Products of Fibred Coarsely Embeddable Spaces

Abstract: In this paper, we prove that the coarse Novikov conjecture holds for finite products of bounded-geometry proper metric spaces whose factors admit fibred coarse embeddings into possibly different target spaces. A key ingredient is the construction of suitable coarsely proper algebras adapted to product spaces. Our other main tool is an iterated approach to relative higher index theory. By constructing the corresponding multi-stage Roe algebras and index maps, we establish a reduction theorem that bridges these iterated relative statements with the global coarse Novikov conjecture.