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ON AN ACTION OF THE BRAID GROUP B_2g+2 ON THE FREE GROUP F_2g

CHRISTIAN KASSEL

Institut de Recherche Mathématique Avancée, CNRS & Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg, France

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https://doi.org/10.1142/S0218196713400110Cited by:2 (Source: Crossref)

Abstract

We construct an action of the braid group B_2g+2 on the free group F_2g extending an action of B₄ on F₂ introduced earlier by Reutenauer and the author. Our action induces a homomorphism from B_2g+2 into the symplectic modular group Sp_2g(ℤ). In the special case g = 2 we show that the latter homomorphism is surjective and determine its kernel, thus obtaining a braid-like presentation of Sp₄(ℤ).

En mi'm alte Kumpel Christophe Reutenauer

Keywords:

AMSC: 20F36, 20E05, 20H05, 11F46, 57M07, 57M12

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