Aspherical word labeled oriented graphs and cyclically presented groups-Reference-Cited by-同舟云学术

Aspherical word labeled oriented graphs and cyclically presented groups

Published:2015-04 Issue:05 Volume:24 Page:1550025
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Harlander Jens¹,Rosebrock Stephan²

Affiliation:

1. Boise State University, Boise, ID, USA

2. Pädagogische Hochschule Karlsruhe, Bismarckstr. 10, 76133 Karlsruhe, Germany

Abstract

A word labeled oriented graph (WLOG) is an oriented graph [Formula: see text] 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021821651550025X

Reference7 articles.

1. J. H. C. Whitehead's Asphericity Question

2. Reducible Diagrams and Equations Over Groups

3. On the asphericity of ribbon disc complements

4. Tadpole Labelled Oriented Graph groups and cyclically presented groups

5. Constructing non-positively curved spaces and groups

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