2017/11/18 by Engel, Alexander, Wulff, Christopher · 1 citation
#20F65 #20F67 #51F30 #57M07 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #K-Theory and Homology (math.KT) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1711.06836
This paper is a systematic approach to the construction of coronas (i.e. Higson dominated boundaries at infinity) of combable spaces. We introduce three additional properties for combings: properness, coherence and expandingness. Properness is the condition under which our construction of the corona works. Under the assumption of coherence and expandingness, attaching our corona to a Rips complex construction yields a contractible σ-compact space in which the corona sits as a Z-set. This results in bijectivity of transgression maps, injectivity of the coarse assembly map and surjectivity of the coarse co-assembly map. For groups we get an estimate on the cohomological dimension of the corona in terms of the asymptotic dimension. Furthermore, if the group admits a finite model for its classifying space BG, then our constructions yield a Z-structure for the group.