On the structure of braid groups on complexes

Byung Hee An; Hyo Won Park

doi:10.1016/j.topol.2017.05.001

On the structure of braid groups on complexes

Byung Hee An, Hyo Won Park

Department of Mathematics Education

Pohang University of Science and Technology

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

2 Scopus citations

Abstract

We consider the braid group B_n(X) on a finite simplicial complex X, which is a generalization of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between geometric decompositions for X and their effects on the braid groups. As applications, we give complete criteria for both the surface embeddability and planarity for X, which are the torsion-freeness of the braid group B_n(X) and its abelianization H₁(B_n(X)), respectively.

Original language	English
Pages (from-to)	86-119
Number of pages	34
Journal	Topology and its Applications
Volume	226
DOIs	https://doi.org/10.1016/j.topol.2017.05.001
State	Published - 1 Aug 2017

Keywords

A complex of groups
Braid groups
Planar embedding

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10.1016/j.topol.2017.05.001

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abstract = "We consider the braid group Bn(X) on a finite simplicial complex X, which is a generalization of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between geometric decompositions for X and their effects on the braid groups. As applications, we give complete criteria for both the surface embeddability and planarity for X, which are the torsion-freeness of the braid group Bn(X) and its abelianization H1(Bn(X)), respectively.",

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AB - We consider the braid group Bn(X) on a finite simplicial complex X, which is a generalization of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between geometric decompositions for X and their effects on the braid groups. As applications, we give complete criteria for both the surface embeddability and planarity for X, which are the torsion-freeness of the braid group Bn(X) and its abelianization H1(Bn(X)), respectively.

KW - A complex of groups

KW - Braid groups

KW - Planar embedding

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EP - 119

JO - Topology and its Applications

JF - Topology and its Applications

ER -

On the structure of braid groups on complexes

Abstract

Keywords

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