Coronas for properly combable spaces

Alexander Engel; Christopher Wulff

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arXiv · 1711.06836

Coronas for properly combable spaces

Alexander Engel·Christopher Wulff

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Abstract

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.

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BibTeX RIS

Alexander Engel, Christopher Wulff. 2021-10-13. Coronas for properly combable spaces. https://arxiv.org/abs/1711.06836

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