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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72269We 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 > 1.14 pagesGroup Theory20F36; 20E05; 20F28; 20G15Extending representations of braid groups to the automorphism groups of free groupstext