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arXiv · 1406.2411

Actions of the n-strand braid groups on the free group of rank n which are similar to the Artin representation

Tetsuya Ito
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Abstract

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 $i$-th generator $\sigma_{i}$ of $B_{n}$ acts so that it fixes all free generators $x_{j}$ except $j = i,i+1$. We determine all such representations and discuss knot invariants coming from such representations.

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Tetsuya Ito. 2014-06-10. Actions of the n-strand braid groups on the free group of rank n which are similar to the Artin representation. https://doi.org/10.1093/qmath%2Fhau033

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