Geodesic
Relative vertex asphericity
Canadian mathematical bulletin, Tome 64 (2021) no. 2, pp. 292-305

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DOI

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 $(L,K)$, 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.
DOI : 10.4153/S0008439520000454
Mots-clés : Diagrammatic reducibility, asphericity, 2-complex, weight test, relative asphericity 
Harlander, Jens; Rosebrock, Stephan. Relative vertex asphericity. Canadian mathematical bulletin, Tome 64 (2021) no. 2, pp. 292-305. doi: 10.4153/S0008439520000454
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     title = {Relative vertex asphericity},
     journal = {Canadian mathematical bulletin},
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     year = {2021},
     volume = {64},
     number = {2},
     doi = {10.4153/S0008439520000454},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000454/}
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