Coronas for properly combable spaces
| Autor: | Christopher Wulff, Alexander Engel |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
media_common.quotation_subject 20F65 20F67 51F30 57M07 010102 general mathematics Metric Geometry (math.MG) Geometric Topology (math.GT) K-Theory and Homology (math.KT) Infinity 01 natural sciences Asymptotic dimension Mathematics - Geometric Topology Mathematics - Metric Geometry 0103 physical sciences Mathematics - K-Theory and Homology FOS: Mathematics Algebraic Topology (math.AT) Astrophysics::Solar and Stellar Astrophysics 010307 mathematical physics Geometry and Topology Mathematics - Algebraic Topology 0101 mathematics Analysis Mathematics media_common |
| Popis: | 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. Comment: v2: minor improvements, 92 pages v3: final version, accepted by Journal of Topology and Analysis |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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