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Homotopy theory for truncated weak equivalences of simplicial groups

Published online by Cambridge University Press:  01 January 1997

ANTONIO R. GARZÓN  and
JESÚS G. MIRANDA
ANTONIO R. GARZÓN
Affiliation:
Departamento de Álgebra, Universidad de Granada, 18071 Granada, Spain
JESÚS G. MIRANDA
Affiliation:
Departamento de Álgebra, Universidad de Granada, 18071 Granada, Spain
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Abstract

In this paper we give for any r, n, 0 [les ] r [les ] n, a Quillen's model structure to the category of simplicial groups where the weak equivalences are those morphisms f[bull] such that πq(f[bull]) is an isomorphism for r [les ] q [les ] n. This is carried out by studying the cases r = 0 and n → ∞ previously and, in each one of them, we make explicit some constructions for the associated homotopy theories, such as the cylinder and path objects and the loop and suspension functors, and we also relate the simplicial homotopy relation to the homotopy relation obtained from these structures.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 121 , Issue 1 , January 1997 , pp. 51 - 74
Copyright
© Cambridge Philosophical Society 1997

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