The Local Structure of Injective LOT-Complexes
Document Type
Article
Publication Date
10-1-2023
Abstract
Labeled oriented trees, LOT’s, encode spines of ribbon discs in the 4-ball and ribbon 2-knots in the 4-sphere. The unresolved asphericity question for these spines is a major test case for Whitehead’s asphericity conjecture. In this paper we give a complete description of the link of a reduced injective LOT complex. An important case is the following: If Γ is a reduced injective LOT that does not contain boundary reducible sub-LOTs, then lk(K(Γ)) is a bi-forest. As a consequence K(Γ) is aspherical, in fact DR, and its fundamental group is locally indicable. We also show that a general injective LOT complex is aspherical. Some of our results have already appeared in print over the last two decades and are collected here.
Publication Information
Harlander, Jens and Rosebrock, Stephan. (2023). "The Local Structure of Injective LOT-Complexes". Topology and Its Applications, 338, 108650. https://doi.org/10.1016/j.topol.2023.108650