On an action of the braid group B_{2g+2} on the free group F_{2g}

Christian Kassel (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We construct an action of the braid group B_{2g+2} on the free group F_{2g} extending an action of B_4 on F_2 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 Sp_4(Z).

Keywords: braid group; free group; symplectic group; ramified covering

Domains: Group Theory [math.GR]; Geometric Topology [math.GT]

Christian Kassel. On an action of the braid group B_{2g+2} on the free group F_{2g}. International Journal of Algebra and Computation, 2013, pp.8-2 (2014), 497--511. ⟨10.1142/S0218196713400110⟩. ⟨hal-00731000⟩