Aspherical word labeled oriented graphs and cyclically presented groups

Jens Harlander; Stephan Rosebrock

doi:10.1142/S021821651550025X

Aspherical word labeled oriented graphs and cyclically presented groups

Jens Harlander
, Stephan Rosebrock

Mathematics Department

Karlsruhe University of Education

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

6 Scopus citations

Abstract

A word labeled oriented graph (WLOG) is an oriented graph G{script} on vertices X = {x₁,⋯,x_n}, where each oriented edge is labeled by a word in X^±1. WLOGs give rise to presentations which generalize Wirtinger presentations of knots. WLOG presentations, where the underlying graph is a tree, are of central importance in view of Whitehead's Asphericity Conjecture. We present a class of aspherical word labeled oriented graphs. This class can be used to produce highly non-injective aspherical labeled oriented trees and also aspherical cyclically presented groups.

Original language	English
Article number	1550025
Journal	Journal of Knot Theory and its Ramifications
Volume	24
Issue number	5
DOIs	https://doi.org/10.1142/S021821651550025X
State	Published - 27 Apr 2015

Keywords

2-complex
asphericity
cyclically presented group
labeled oriented graph
Labeled oriented tree

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10.1142/S021821651550025X

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title = "Aspherical word labeled oriented graphs and cyclically presented groups",

abstract = "A word labeled oriented graph (WLOG) is an oriented graph G\{script\} on vertices X = \{x1,⋯,xn\}, where each oriented edge is labeled by a word in X±1. WLOGs give rise to presentations which generalize Wirtinger presentations of knots. WLOG presentations, where the underlying graph is a tree, are of central importance in view of Whitehead's Asphericity Conjecture. We present a class of aspherical word labeled oriented graphs. This class can be used to produce highly non-injective aspherical labeled oriented trees and also aspherical cyclically presented groups.",

keywords = "2-complex, asphericity, cyclically presented group, labeled oriented graph, Labeled oriented tree",

author = "Jens Harlander and Stephan Rosebrock",

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AB - A word labeled oriented graph (WLOG) is an oriented graph G{script} on vertices X = {x1,⋯,xn}, where each oriented edge is labeled by a word in X±1. WLOGs give rise to presentations which generalize Wirtinger presentations of knots. WLOG presentations, where the underlying graph is a tree, are of central importance in view of Whitehead's Asphericity Conjecture. We present a class of aspherical word labeled oriented graphs. This class can be used to produce highly non-injective aspherical labeled oriented trees and also aspherical cyclically presented groups.

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KW - asphericity

KW - cyclically presented group

KW - labeled oriented graph

KW - Labeled oriented tree

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JF - Journal of Knot Theory and its Ramifications

IS - 5

M1 - 1550025

ER -

Aspherical word labeled oriented graphs and cyclically presented groups

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Keywords

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