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For m >= n > 0, a map f between pointed spaces is said to be a weak [n,m]-equivalence if f induces isomorphisms of the homotopy groups \pi_k for n <= k <= m~. Associated with this notion we give two different closed model category structures to the category of pointed spaces. Both structures have the same class of weak equivalences but different classes of fibrations and therefore of cofibrations. Using one of these structures, one obtains that the localized category is equivalent to the category of n-reduced CW-complexes with dimension less than or equal to m+1 and m-homotopy classes of cellular pointed maps. Using the other structure we see that the localized category is also equivalent to the homotopy category of (n-1)-connected (m+1)-coconnected CW-complexes.
@article{TAC_1997_3_a9,
author = {J. Ignacio Extremiana Aldana and Luis J. Hernandez Paricio and Maria T. Rivas Rodriguez},
title = {Closed model categories for $[n,m]$-types},
journal = {Theory and applications of categories},
pages = {251--268},
publisher = {mathdoc},
volume = {3},
year = {1997},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_1997_3_a9/}
}
TY - JOUR AU - J. Ignacio Extremiana Aldana AU - Luis J. Hernandez Paricio AU - Maria T. Rivas Rodriguez TI - Closed model categories for $[n,m]$-types JO - Theory and applications of categories PY - 1997 SP - 251 EP - 268 VL - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TAC_1997_3_a9/ LA - en ID - TAC_1997_3_a9 ER -
%0 Journal Article %A J. Ignacio Extremiana Aldana %A Luis J. Hernandez Paricio %A Maria T. Rivas Rodriguez %T Closed model categories for $[n,m]$-types %J Theory and applications of categories %D 1997 %P 251-268 %V 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TAC_1997_3_a9/ %G en %F TAC_1997_3_a9
J. Ignacio Extremiana Aldana; Luis J. Hernandez Paricio; Maria T. Rivas Rodriguez. Closed model categories for $[n,m]$-types. Theory and applications of categories, Tome 3 (1997), pp. 251-268. http://geodesic.mathdoc.fr/item/TAC_1997_3_a9/