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We consider the inclusion i: F\\_n(M) --\\textgreater{} M^n of the nth configuration space F\\_n(M) of M into the n-fold Cartesian product of M, as well as the induced homomorphism i\\_\\#: P\\_n(M) --\\textgreater{} (\\pi\\_1(M))^n, where P\\_n(M) is the n-string pure braid group of M. Both i and i\\_\\# were studied initially by J.Birman who conjectured that Ker(i\\_\\#) is equal to the normal closure of the Artin pure braid group P\\_n in P\\_n(M). 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