Abelian quotients for groups generated by cubed half-twists
Abstract
Below we construct non-cyclic and torsion-free abelian quotients for subgroups of braid groups generated by cube powers of half-twists. In the case of 3 and 4 strands we compute the abelianization of these groups. Also, we get abelianizations of level-3 congruence subgroups of braid groups on 3 and 4 strands. Moreover, we construct non-cyclic and torsion-free abelian quotients for level-3 congruence subgroups of braid groups. The constructions are based on the original construction of Dennis Johnson \cite{DJ}, who computed an abelian quotient of the Torelli group.
Keywords
Cite
@article{arxiv.2305.08639,
title = {Abelian quotients for groups generated by cubed half-twists},
author = {Charalampos Stylianakis},
journal= {arXiv preprint arXiv:2305.08639},
year = {2023}
}
Comments
Proof of Theorem 5.4 is wrong. In particular, the map that is claimed to be a homomorphism, it is not a homomorphism. Also, some of the main results of the paper rely on that Theorem