Freeness Conditions for 2-Crossed Modules and Complexes

Freeness Conditions for 2-Crossed Modules and Complexes (1998)

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by A. Mutlu , T. Porter

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@MISC{Mutlu98freenessconditions,
    author = {A. Mutlu and T. Porter},
    title = {Freeness Conditions for 2-Crossed Modules and Complexes},
    year = {1998}
}

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Abstract

Using free simplicial groups, it is shown how to construct a free or totally free 2-crossed module on suitable construction data. 2-crossed complexes are introduced and similar freeness results for these are discussed. A. M. S. Classication: 18D35 18G30 18G50 18G55. Introduction Crossed modules were introduced by Whitehead in [23] with a view to capturing the relationship between 1 and 2 of a space. Homotopy systems (which would now be called free crossed complexes [5] or totally free crossed chain complexes (cf. Baues [3, 4]) were introduced, again by Whitehead, to incorporate the action of 1 on the higher relative homotopy groups of a CW-complex. They consist of a crossed module at the base and a chain complex of modules over 1 further up. Conduche [9] dened 2-crossed modules as a model of connected 3-types and showed how to obtain a 2-crossed module from a simplicial group. A variant of 2-crossed modules are the quadratic modules of Baues [3, 4] and he also denes a not...

Citations

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