On Burau representations at roots of unity

Details On Burau representations at roots of unity On Burau representations at roots of unity

2009-07-03

arxiv.org/abs/0907.0568v4

Mathematics

Geometric Topology

18p. Former arXiv:0907.0568 is now split as two separate papers: this one records the first half and the title is changed acco

Scientific paper

We consider subgroups of the braid groups which are generated by $k$-th powers of the standard generators and prove that any infinite intersection (with even $k$) is trivial. This is motivated by some conjectures of Squier concerning the kernels of Burau's representations of the braid groups at roots of unity. Furthermore, we show that the image of the braid group on 3 strands by these representations is either a finite group, for a few roots of unity, or a finite extension of a triangle group, by using geometric methods.

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