Generalized Long-Moody functors

Abstract : In this paper, we generalize the Long-Moody construction for braid groups to other families of groups, such as automorphism groups of free groups, mapping class groups of orientable and non-orientable surfaces or mapping class groups of 3-manifolds. Fixing an appropriate family of groups, we define endo-functors, called Long-Moody functors, between the category of functors from the homogeneous category associated with the family of groups to a module category. We prove that under some extra assumptions the Long-Moody functors increase by one the degree of (very) strong and weak polynomiality of functors. For the particular case of braid groups, we recover a result previously obtained by the author.
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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01585778
Contributeur : Arthur Soulié <>
Soumis le : mardi 12 septembre 2017 - 08:34:44
Dernière modification le : jeudi 14 septembre 2017 - 01:01:44

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  • HAL Id : hal-01585778, version 1
  • ARXIV : 1709.04278

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Arthur Soulié. Generalized Long-Moody functors. 2017. 〈hal-01585778〉

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