Aspherical Word Labeled Oriented Graphs and Cyclically Presented Groups

2014/08/17 by Jens Harlander, Harlander, Jens, Stephan Rosebrock +1
Computer Science · Mathematics · #20F05 #57M05 #57M20 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1408.3805

openalex publication_date 2014/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A \em word labeled oriented graph (WLOG) is an oriented graph \cal G on vertices X=\ x₁,… ,x_k\, 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.

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