Engel, Alexander and Wulff, Christopher (2023) Coronas for properly combable spaces. JOURNAL OF TOPOLOGY AND ANALYSIS, 15 (04). pp. 953-1035. ISSN 1793-5253, 1793-7167
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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 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ARTIN GROUPS; K-THEORY; NOVIKOV CONJECTURES; BOUNDED COHOMOLOGY; BOUNDARIES; DIMENSION; HOMOLOGY; COMPLEXES; ALGEBRAS; SYSTEMS; Combings; Z-boundaries; coronas; coarse assembly map; asymptotic dimension; coarse homology theories; transgression maps; non-positively curved spaces and groups |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 19 Apr 2024 16:02 |
| Last Modified: | 19 Apr 2024 16:02 |
| URI: | https://pred.uni-regensburg.de/id/eprint/61627 |
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