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Theses

Produit tensoriel non abélien, relations entre commutateurs et homologie des groupes

Abstract : The non-abelian tensor product based on a couple of crossed modules on the same group is in surjection on the commutator sub-group induced by the images of the crossed modules. The factorisations through the crossed modules define generalised commutators. The associated kernels are quotients of groups of relations between commutators by universal relations. Such quotients give all the homology of a group extending results on the second (Miller) and third (Brown-Loday and Ellis) homology. We obtain some of this quotients or some links between them by studying identities in tensor product, right exactness and obstruction to left exactness. This questions are also connected to the construction of sections respecting crossed modules laws and to the nullity of canonical morphisms induced by the lower central serie on third homology.
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https://tel.archives-ouvertes.fr/tel-00009663
Contributor : Gwenaël Guérard <>
Submitted on : Monday, July 4, 2005 - 4:34:51 PM
Last modification on : Thursday, January 7, 2021 - 4:13:11 PM
Long-term archiving on: : Friday, April 2, 2010 - 10:43:23 PM

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  • HAL Id : tel-00009663, version 1

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Gwenaël Guérard. Produit tensoriel non abélien, relations entre commutateurs et homologie des groupes. Mathématiques [math]. Université Rennes 1, 2005. Français. ⟨tel-00009663⟩

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