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

M. Teicher

doi:10.1016/s0166-8641(96)00154-x

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

M. Teicher

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 B̃_n and refer to the groups which admit an action of B̃_n as B̃_n-groups. The group B̃_n is an extension of a solvable group by a symmetric group. We distinguish special elements in B̃_n-groups which we call prime elements and we give a criterion for an element to be prime. B̃_n-groups appear as fundamental groups of complements of branch curves.

Original language	English
Pages (from-to)	153-186
Number of pages	34
Journal	Topology and its Applications
Volume	78
Issue number	1-2
DOIs	https://doi.org/10.1016/s0166-8641(96)00154-x
State	Published - 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].

Funders	Funder number
Emmy Noether Research Institute for Mathematics
Minerva Foundation

Keywords

Braid group

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10.1016/s0166-8641(96)00154-x

Cite this

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AU - Teicher, M.

N1 - Funding Information: ~' This research was partially supported by the Minerva Foundation from Germany and the Emmy Noether Research Institute. I E-mail: [email protected].

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

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

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