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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A closed model category
for ($n-1$)-connected spaces


Authors: J. Ignacio Extremiana Aldana, L. Javier Hernández Paricio and M. Teresa Rivas Rodríguez
Journal: Proc. Amer. Math. Soc. 124 (1996), 3545-3553
MSC (1991): Primary 55P15, 55U35
MathSciNet review: 1353370
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Abstract: For each integer $n > 0$, 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 $(n-1)$-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 $n>0$, 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 $q\ge n$ .


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Additional Information

J. Ignacio Extremiana Aldana
Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain
Email: jextremi@siur.unirioja.es

L. Javier Hernández Paricio
Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
Email: ljhernan@posta.unizar.es

M. Teresa Rivas Rodríguez
Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03606-4
PII: S 0002-9939(96)03606-4
Keywords: Closed model category, homotopy category, $(n-1)$-connected space
Received by editor(s): May 5, 1995
Additional Notes: The authors acknowledge the financial aid given by the U.R., I.E.R. and DGICYT, project PB93-0581-C02-01.
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1996 American Mathematical Society