Coronas for properly combable spaces

This paper is a systematic approach to the construction of coronas (i.e. Higson dominated boundaries at infinity) combable spaces. We introduce three additional properties for combings: properness, coherence and expandingness. Properness condition under which our corona works. Under assumption expandingness, attaching Rips complex yields contractible [Formula: see text]-compact space in sits as text]-set. results bijectivity transgression maps, injectivity coarse assembly map surjectivity co-assembly map. For groups we get an estimate on cohomological dimension terms asymptotic dimension. Furthermore, if group admits finite model its classifying text], then constructions yield text]-structure group.