Internat. J. Algebra Comput. 23, (2013) 819-831, doi:10.1142/S0218196713400110 - arXiv:1204.2377

Christian Kassel

On an action of the braid group B_2g+2 on the free group F_2g

Mathematics Subject Classification (2010): Primary 20F36, 20E05, 20H05, Secondary 11F46, 57M07, 57M12

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-type presentation of Sp₄(Z).

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(29 juin 2013)