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

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Abstract

This paper presents and describes a quotient of the Artin braid group by commutators of transversal half-twists and investigates its group actions. We denote the quotient by B̃n and refer to the groups which admit an action of B̃n as B̃n-groups. The group B̃n is an extension of a solvable group by a symmetric group. We distinguish special elements in B̃n-groups which we call prime elements and we give a criterion for an element to be prime. B̃n-groups appear as fundamental groups of complements of branch curves.

Original languageEnglish
Pages (from-to)153-186
Number of pages34
JournalTopology and its Applications
Volume78
Issue number1-2
DOIs
StatePublished - 1997

Bibliographical note

Funding Information:
~' This research was partially supported by the Minerva Foundation from Germany and the Emmy Noether Research Institute. I E-mail: [email protected].

Funding

~' This research was partially supported by the Minerva Foundation from Germany and the Emmy Noether Research Institute. I E-mail: [email protected].

FundersFunder number
Emmy Noether Research Institute
Minerva Foundation

    Keywords

    • Braid group

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