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

Muro, Fernando

doi:10.1090/S0002-9947-04-03597-4

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

Trans. Amer. Math. Soc. 357 (2005), 3623-3653

DOI: https://doi.org/10.1090/S0002-9947-04-03597-4

Published electronically: 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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