Cohomological approach to asymptotic dimension
| dc.creator | Dranishnikov, A. N. | |
| dc.date | 2006-08-09 | |
| dc.date.accessioned | 2026-07-07T07:21:34Z | |
| dc.date.available | 2026-07-07T07:21:34Z | |
| dc.description | We introduce the notion of asymptotic cohomology based on the bounded cohomology and define cohomological asymptotic dimension $\as_{\Z} X$ of metric spaces. We show that it agrees with the asymptotic dimension $\as X$ when the later is finite. Then we use this fact to construct an example of a metric space $X$ of bounded geometry with finite asymptotic dimension for which $\as(X\times\R)=\as X$. In particular, it follows for this example that the coarse asymptotic dimension defined by means of Roe's coarse cohomology is strictly less than its asymptotic dimension. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/math/0608215 | |
| dc.identifier | http://arxiv.org/abs/math/0608215 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115341 | |
| dc.subject | Metric Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 55M10, 20F69, 51F99, 57M20 | |
| dc.title | Cohomological approach to asymptotic dimension | |
| dc.type | text |