Relative Vertex Asphericity
Geometric Topology
2021-07-01 v2 Group Theory
Abstract
Diagrammatic 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 , where is a subcomplex of . 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.
Keywords
Cite
@article{arxiv.1912.12512,
title = {Relative Vertex Asphericity},
author = {Jens Harlander and Stephan Rosebrock},
journal= {arXiv preprint arXiv:1912.12512},
year = {2021}
}