Aspherical Word Labeled Oriented Graphs and Cyclically Presented Groups

Jens Harlander; Stephan Rosebrock

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arXiv · 1408.3805

Aspherical Word Labeled Oriented Graphs and Cyclically Presented Groups

Jens Harlander·Stephan Rosebrock

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Abstract

A {\em word labeled oriented graph} (WLOG) is an oriented graph $\cal G$ on vertices $X=\{ x_1,\ldots ,x_k\}$, where each oriented edge is labeled by a word in $X^{\pm1}$. 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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Jens Harlander, Stephan Rosebrock. 2014-08-17. Aspherical Word Labeled Oriented Graphs and Cyclically Presented Groups. https://arxiv.org/abs/1408.3805

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