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Égalité de Andreadakis et représentation pour des groupes de tresses généralisées

Abstract : The pure welded braid group on n-strands or McCool group PΣn has families of subgroups such as the ordinary pure braid group Pn, the upper triangular McCool group PΣ+n and the partial inner automorphisms group In. It is established that the Andreadakis filtration restricted to PΣ^+_n and the Andreadakis filtration restricted to Pn coincide each with its lower central serie. We prove a similar result for In and we also establish an isomorphism between In and the inner automorphism group Int(PΣ^+_{n+1}) of PΣ^+_{n+1}.We then construct a variant of the Burau representation of the virtual braid group on n-strands VBn which does not factorize into a representation of the group of welded braids WBn. Finally, in the case of the pure welded braids group or McCool group PΣn, we propose an iterative procedure to that of the Long-Moody method which allows to construct a faithful matrix representation of PΣn thus generalizing an extension of the Gassner representation of Pn.
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Submitted on : Thursday, March 17, 2022 - 5:16:04 PM
Last modification on : Friday, August 5, 2022 - 10:51:51 AM
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  • HAL Id : tel-03612393, version 1

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Abdoulrahim Ibrahim Youssouf. Égalité de Andreadakis et représentation pour des groupes de tresses généralisées. Topologie algébrique [math.AT]. Université Montpellier, 2021. Français. ⟨NNT : 2021MONTS056⟩. ⟨tel-03612393⟩

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