Transactions of the American Mathematical Society

Suspensions of crossed and quadratic complexes, co-H-structures and applications

Author(s): Fernando Muro
Journal: Trans. Amer. Math. Soc. 357 (2005), 3623-3653.
MSC (2000): Primary 55P40, 55P45, 55P65; Secondary 55U15, 20F14, 20F18, 20J05
Posted: December 9, 2004
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Abstract: Crossed and quadratic modules are algebraic models of the 2-type and the 3-type of a space, respectively. In this paper we compute a purely algebraic suspension functor from crossed to quadratic modules which sends a 2-type to the 3-type of its suspension. We also give some applications in homotopy theory and group theory.

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Fernando Muro
Affiliation: Departamento de Geometría y Topología, Universidad de Sevilla, Apartado de Correos 1160, 41080 Sevilla, Spain
Email: fmuro@us.es

DOI: 10.1090/S0002-9947-04-03597-4
PII: S 0002-9947(04)03597-4
Received by editor(s): February 19, 2003
Received by editor(s) in revised form: December 30, 2003
Posted: December 9, 2004
Additional Notes: The author was partially supported by the MCyT grant BFM2001-3195-C02-01 and the MECD FPU fellowship AP2000-3330.
Copyright of article: Copyright 2004, American Mathematical Society

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