Topological Model Categories Generated By Finite Complexes
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- A. "Alex" Chigogidze, Professor and Department Chair (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
Abstract: Our main result states that for each finite complex L the category 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 = {point}. The other – describing n-homotopy equivalences between at most (n + 1)-
dimensional CW-complexes as maps inducing isomorphisms of k-dimensional homotopy groups with k = n – by letting L = Sn+1, n = 0.
Topological Model Categories Generated By Finite Complexes
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Created on 1/1/2002
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Additional Information
- Publication
- arXiv:math/0205014v2 [math.AT] 31 Jul 2002
- Language: English
- Date: 2002
- Keywords
- Model category, [L]–homotopy, [L]-com