On the quotient of the braid group by commutators of transversal\n half-twists and its group actions

1997/03/20 by Mina Teicher, Teicher, Mina
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.alg-geom/9703025

openalex publication_date 1997/03/20 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

The group described in this paper appeared while studying fundamental groups\nof complements of branch curves. It turned out that a certain quotient of the\nbraid group acts on those fundamental groups and studying this action is\nessential for understanding the structure of the fundamental groups. We\ndescribe here the quotient of the Artin braid group by commutators of\ntransversal half-twists and we investigates its group actions. We denote the\nquotient by B_n~ and refer to the groups which admit an action of B_n~ , as\nB_n~-groups.\n We distinguish special elements in B_n~-groups which we call prime elements\nand we give a criterion for an element to be prime. This criterion will be\napplied to the study of the structure of fundamental groups of complements of\nbranch curves. The group B_n~ itself turns out to be an extension of a solvable\ngroup by a symmetric group.\n

Related

• Identifying Powers of Half-Twists and Computing its Root
• Braid Group, Algebraic Surfaces and Fundamental Groups of complements of Branch Curves
• On certain permutation representations of the braid group
• A quotient of the braid group related to pseudosymmetric braided categories
• Quotients of the Artin braid groups and crystallographic groups