# Members & Guests

## Dr. Christopher Wulff

Georg-August-Universität Göttingen

E-mail: christopher.wulff(at)mathematik.uni-goettingen.de
Telephone: +49 551 39-7751
Homepage: http://www.uni-math.gwdg.de/cwulff/

## Project

10Duality and the coarse assembly map

## Publications within SPP2026

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 $$\sigma$$-compact space in which the corona sits as a $$\mathbb{Z}$$-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 $$\mathbb{Z}$$-structure for the group.