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

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by A. Mutlu , T. Porter
Citations:2 - 2 self
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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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28 Simplicial methods and the interpretation of triple cohomology - Duskin
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10 Homotopy types, in Handbook of Algebraic Topology - Baues - 1995
6 A relation between CW-complex and free c.s.s groups - Kan - 1959
5 Varieties of Simplicial Groupoids, I: Crossed Complexes - Ehlers, Porter - 1997
5 Pairings in the Moore Complex of a Simplicial Group - Mutlu, Peiffer - 1997
4 Simplicial T -Complexes: a non abelian version of a theorem of - Ashley - 1988
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2 Identities among relations, Low dimension topology - Brown, Huesbschmann - 1982
2 Spaces having many non-trivial homotopy groups - Loday - 1982
2 Applications of Peier pairings in the Moore complex of a simplicial group - Mutlu, Porter - 1997
2 On combinatorial descriptions of (K(; 1)), MSRI preprint 069 - Wu - 1995
1 Free crossed resolution from a simplicial group with given CW -basis - Mutlu, Porter - 1997
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