Aspherical Word Labeled Oriented Graphs and Cyclically Presented Groups
Jens Harlander, Stephan Rosebrock

TL;DR
This paper introduces a class of aspherical word labeled oriented graphs (WLOGs) that generalize knot presentations and can generate aspherical cyclically presented groups, advancing understanding of Whitehead's Asphericity Conjecture.
Contribution
The paper presents a new class of aspherical WLOGs, expanding the toolkit for constructing aspherical groups and exploring their properties.
Findings
Constructed a class of aspherical WLOGs.
Produced highly non-injective aspherical labeled oriented trees.
Generated aspherical cyclically presented groups.
Abstract
A {\em word labeled oriented graph} (WLOG) is an oriented graph on vertices , where each oriented edge is labeled by a word in . 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 world 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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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · semigroups and automata theory
