Remarks on the faithfulness of the Jones representations

Details Remarks on the faithfulness of the Jones representations Remarks on the faithfulness of the Jones representations

2008-03-03

arxiv.org/abs/0803.0304v1

Mathematics

Geometric Topology

9 pages

Scientific paper

We consider the linear representations of the mapping class group of an n-punctured 2-sphere constructed by V. F. R. Jones using Iwahori-Hecke algebras of type A. We show that their faithfulness is equivalent to that of certain related Iwahori-Hecke algebra representation of Artin's braid group of n-1 strands. In the case of n=6, we provide a further restriction for the kernel using our previous result, as well as a certain relation to the Burau representation of degree 4.

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