Topological model categories generated by finite complexes
| dc.creator | Chigogidze, A. | |
| dc.creator | Karasev, A. | |
| dc.date | 2002-05-01 | |
| dc.date | 2002-07-31 | |
| dc.date.accessioned | 2026-07-07T04:48:12Z | |
| dc.date.available | 2026-07-07T04:48:12Z | |
| dc.description | Our main result states that for each finite complex L the category ${\bf TOP}$ of topological spaces possesses a model category structure (in the sense of Quillen) whose weak equivalences are precisely maps which induce isomorphisms of all [L]-homotopy groups. The concept of [L]-homotopy has earlier been introduced by the first author and is based on Dranishnikov's notion of extension dimension. As a corollary we obtain an algebraic characterization of [L]-homotopy equivalences between [L]-complexes. This result extends two classical theorems of J. H. C. Whitehead. One of them -- describing homotopy equivalences between CW-complexes as maps inducing isomorphisms of all homotopy groups -- is obtained by letting $L = \{{\rm point}\}$. The other -- describing n-homomotopy equivalences between at most $(n+1)$-dimensional CW-complexes as maps inducing isomorophisms of k-dimensional homotopy groups with $k \leq n$ -- by letting $L = S^{n+1}$, $n \geq 0$. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0205014 | |
| dc.identifier | http://arxiv.org/abs/math/0205014 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63956 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Category Theory | |
| dc.subject | 55U40, 18D15 | |
| dc.title | Topological model categories generated by finite complexes | |
| dc.type | text |