A closed model category

for ()-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

DOI:
https://doi.org/10.1090/S0002-9939-96-03606-4

MathSciNet review:
1353370

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Abstract | References | Similar Articles | Additional Information

Abstract: For each integer , we give a distinct closed model category structure to the category of pointed spaces such that the corresponding localized category is equivalent to the standard homotopy category of -connected CW-complexes. The structure of closed model category given by Quillen to is based on maps which induce isomorphisms on all homotopy group functors 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 for .

**[1]**J.G. Cabello, A.R. Garzón,*Closed model structures for algebraic models of -types*, J. Pure Appl. Algebra**103**(1995), 287--302.**[2]**C. Elvira, L.J. Hernández,*Closed model categories for the -type of spaces and simplicial sets*, Math. Proc. Camb. Phil. Soc**118**(1995), 93-103. CMP**95:12****[3]**P. Gabriel, M. Zisman,*Calculus of fractions and homotopy theory*, Springer-Verlag, Berlin, New York, 1967. MR**35:1019****[4]**A.R. Garzón, J.G. Miranda,*Homotopy types of simplicial groups and related closed model structures*, Preprint (1994).**[5]**L.J. Hernández, T. Porter,*Categorical models of -types for pro-crossed complexes and -prospaces*, Lecture Notes in Math**1509**(1992), 146-186. MR**93m:55015****[6]**T. Porter,*-types of simplicial groups and crossed -cubes*, Topology.**32**(1993), 5-24. MR**94e:55017****[7]**D. Quillen,*Homotopical Algebra*, Lecture Notes in Math**43**(1967). MR**36:6480****[8]**D. Quillen,*Rational Homotopy Theory*, Ann. of Maths**90**(1969), 205-295. MR**41:2678**

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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:
https://doi.org/10.1090/S0002-9939-96-03606-4

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