On the kernel of the Gassner representation
KP Knudson - Archiv der Mathematik, 2005 - Springer
Archiv der Mathematik, 2005•Springer
… We study the Gassner representation of the pure braid group Pn by considering its
restriction to a free subgroup F. The kernel of the restriction is shown to lie in the subgroup [
3F,2F], sharpening a result of Lipschutz. … n ]) the unreduced Gassner representation of the
pure braid group Pn (a formula is given in Section 2 below). The faithfulness of Gn for n ≧ 4
is a long-standing open question. In this note, we investigate this by considering the
restriction of Gn to a certain free subgroup Fn−1 of Pn: …
restriction to a free subgroup F. The kernel of the restriction is shown to lie in the subgroup [
3F,2F], sharpening a result of Lipschutz. … n ]) the unreduced Gassner representation of the
pure braid group Pn (a formula is given in Section 2 below). The faithfulness of Gn for n ≧ 4
is a long-standing open question. In this note, we investigate this by considering the
restriction of Gn to a certain free subgroup Fn−1 of Pn: …
Abstract
We study the Gassner representation of the pure braid group P n by considering its restriction to a free subgroup F. The kernel of the restriction is shown to lie in the subgroup [Γ3F, Γ2F], sharpening a result of Lipschutz.
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