TY - JOUR
T1 - Ribbon 2–knot groups of Coxeter type
AU - Harlander, Jens
AU - Rosebrock, Stephan
N1 - Publisher Copyright:
© 2023 MSP (Mathematical Sciences Publishers).
PY - 2023
Y1 - 2023
N2 - Wirtinger presentations of deficiency 1 appear in the context of knots, long virtual knots, and ribbon 2–knots. They are encoded by labeled oriented trees and, for that reason, are also called LOT presentations. These presentations are a well known and important testing ground for the validity (or failure) of Whitehead’s asphericity conjecture. We define LOTs of Coxeter type and show that for every given n there exists a prime LOT of Coxeter type with group of rank n. We also show that label separated Coxeter LOTs are aspherical.
AB - Wirtinger presentations of deficiency 1 appear in the context of knots, long virtual knots, and ribbon 2–knots. They are encoded by labeled oriented trees and, for that reason, are also called LOT presentations. These presentations are a well known and important testing ground for the validity (or failure) of Whitehead’s asphericity conjecture. We define LOTs of Coxeter type and show that for every given n there exists a prime LOT of Coxeter type with group of rank n. We also show that label separated Coxeter LOTs are aspherical.
KW - 2–knots
KW - asphericity
KW - Coxeter groups
KW - knot groups
KW - labeled oriented trees
KW - LOT presentations
KW - Wirtinger presentations
UR - http://www.scopus.com/inward/record.url?scp=85171860590&partnerID=8YFLogxK
U2 - 10.2140/agt.2023.23.2715
DO - 10.2140/agt.2023.23.2715
M3 - Article
AN - SCOPUS:85171860590
SN - 1472-2747
VL - 23
SP - 2715
EP - 2733
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 6
ER -