Extending representations of braid groups to the automorphism groups of free groups

Details Extending representations of braid groups to the automorphism groups of free groups Extending representations of braid groups to the automorphism groups of free groups

2004-08-24

arxiv.org/abs/math/0408330v1

Mathematics

Group Theory

14 pages

Scientific paper

We construct a linear representation of the group IA(F_n) of IA-automorphisms of a free group F_n, an extension of the Gassner representation of the pure braid group P_n. Although the problem of faithfulness of the Gassner representation is still open for n > 3, we prove that the restriction of our representation to the group of basis conjugating automorphisms Cb_n contains a non-trivial kernel even if n=2. We construct also an extensions of the Burau representation to the group of conjugating automorphisms C_n. This representation is not faithful for n > 1.

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