Author:
Harlander Jens,Rosebrock Stephan
Abstract
AbstractDiagrammatic reducibility DR and its generalization, vertex asphericity VA, are combinatorial tools developed for detecting asphericity of a 2-complex. Here we present tests for a relative version of VA that apply to pairs of 2-complexes
$(L,K)$
, where K is a subcomplex of L. We show that a relative weight test holds for injective labeled oriented trees, implying that they are VA and hence aspherical. This strengthens a result obtained by the authors in 2017 and simplifies the original proof.
Publisher
Canadian Mathematical Society
Cited by
2 articles.
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1. The local structure of injective LOT-complexes;Topology and its Applications;2023-10
2. Directed diagrammatic reducibility;Topology and its Applications;2020-08