Slant products on the Higson–Roe exact sequence

We construct a slant product $/ \colon \mathrm{S}_p(X \times Y) \mathrm{K}_{1-q}(\mathfrak{c}^{\mathrm{red}}Y) \to \mathrm{S}_{p-q}(X)$ on the analytic structure group of Higson and Roe K-theory stable corona Emerson Meyer. The latter is domain co-assembly map $\mu^\ast \mathrm{K}_{1-\ast}(\mathfrak{c}^{\mathrm{red}}Y) \mathrm{K}^\ast(Y)$. obtain such products entire Higson--Roe sequence. They imply injectivity results for external maps. Our apply to with aspherical manifolds whose fundamental groups admit coarse embeddings into Hilbert space. To conceptualize class where this method applies, we say that complete $\mathrm{spin}^{\mathrm{c}}$-manifold Higson-essential if its detected by map. prove coarsely hypereuclidean are Higson-essential. draw conclusions positive scalar curvature metrics spaces, particularly non-compact manifolds. also equivariant versions our constructions discuss related problems exactness amenability corona.