On the quotients of coarse structures and Roe algebras (Q2172643)

The paper deals with quotients of the Roe algebras of uniformly locally finite coarse spaces (not necessarily metrizable). The coarse quotient structure of a coarse structure associated to an ideal is introduced and studied. It is shown that the functor that maps a coarse subspace to the quotient of the Roe algebra associated to any ideal forms a cosheaf with values in the category of \(C^*\)-algebras. Finally, the coarse Mayer-Vietoris theorem is proved for relative Roe algebras associated to a pair of coarse subspaces.