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A closed model category for ()-connected spaces

Authors:	J Ignacio Extremiana Aldana L Javier Herná ndez Paricio M Teresa Rivas Rodrí guez

Institution:	Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain ; Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain ; Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain

Abstract:	For each integer , we give a distinct closed model category structure to the category of pointed spaces $\mathop {\mathrm {Top}}\nolimits _{\star }$ such that the corresponding localized category $\mathop {\mathrm {Ho}}\nolimits ( \mathop {\mathrm {Top}}\nolimits _{\star }^{n})$ is equivalent to the standard homotopy category of -connected CW-complexes. The structure of closed model category given by Quillen to $\mathop {\mathrm {Top}}\nolimits _{\star }$ is based on maps which induce isomorphisms on all homotopy group functors $\pi _{q}$ and for any choice of base point. For each , the closed model category structure given here takes as weak equivalences those maps that for the given base point induce isomorphisms on $\pi _{q}$ for $q\ge n$ .

Keywords:	Closed model category homotopy category $(n-1)$-connected space

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