Automorphisms of Pure Sphere Braid Groups and Galois Representations
Let Pn be the pure braid group of the 2-sphere, with n strings (n ≥ 3), and \( \hat P_n \) be its pro-ℓ completion (ℓ: a fixed prime number). We shall study what we call the special automorphism groups of Pn and \( \hat P_n \), and apply it to Galois representations of the type proposed in Grothendieck .
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