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The reduced Gassner representation restricted to a normal free subgroup of the pure braid group

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Abstract.

We show that the reduced Gassner representation restricted to a normal free subgroup U n of the pure braid group, P n , is essentially the Magnus representation of U n / U '' n provided that the indeterminate y, used in defining this representation, is set to be one. Then, as a corollary, Lipschutz's result follows easily that is, in general, the kernel of the reduced Gassner representation restricted to U n is a subgroup of U '' n .

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  1. Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, U.S.A., , , , , , US

    Mohammad N. Abdulrahim

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  1. Mohammad N. Abdulrahim
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Received: 10.5.1996

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Abdulrahim, M. The reduced Gassner representation restricted to a normal free subgroup of the pure braid group. Arch. Math. 69, 8–12 (1997). https://doi.org/10.1007/s000130050087

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  • DOI: https://doi.org/10.1007/s000130050087

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