Actions of The N-Strand Braid Groups on The Free Group of Rank N Which Are Similar to the Artin Representation

ito, tetsuya;

We classify an action of the n-strand braid group on the free group of rank n, which is similar to the Artin representation in the sense that the ith generator σi of Bn acts so that it fixes all free generators xj except j = i, i + 1.We determine all such representations and discuss knot invariants coming from such representations.