Aspherical Word Labeled Oriented Graphs and Cyclically Presented Groups

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A word labeled oriented graph (WLOG) is an oriented graph 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 world labeled oriented graphs. This class can be used to produce highly non-injective aspherical labeled oriented trees and also aspherical cyclically presented groups.

Electronic version of an article published as: Journal of Knot Theory and Its Ramifications, 24(5), 1550025. © 2015, World Scientific Publishing Company. doi: 10.1142/S021821651550025X