TY - JOUR
T1 - Aspherical word labeled oriented graphs and cyclically presented groups
AU - Harlander, Jens
AU - Rosebrock, Stephan
N1 - Publisher Copyright:
© 2015 World Scientific Publishing Company.
PY - 2015/4/27
Y1 - 2015/4/27
N2 - A word labeled oriented graph (WLOG) is an oriented graph G{script} 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.
AB - A word labeled oriented graph (WLOG) is an oriented graph G{script} 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.
KW - 2-complex
KW - asphericity
KW - cyclically presented group
KW - labeled oriented graph
KW - Labeled oriented tree
UR - http://www.scopus.com/inward/record.url?scp=84929881395&partnerID=8YFLogxK
U2 - 10.1142/S021821651550025X
DO - 10.1142/S021821651550025X
M3 - Article
AN - SCOPUS:84929881395
SN - 0218-2165
VL - 24
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
IS - 5
M1 - 1550025
ER -