Abelian quotients for groups generated by cubed half-twists

2023/05/15 by Stylianakis, Charalampos
#20F36 #20K15 #57K20 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2305.08639

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 \citeDJ, who computed an abelian quotient of the Torelli group.

Related

• Powers of half-twists and congruence subgroups of braid groups
• The 3-strand braid group with torsion
• Homotopy braid groups are torsion-free
• On the quotient of the braid group by commutators of transversal\n half-twists and its group actions
• Torsion subgroups of quasi-abelianized braid groups