TY - JOUR
T1 - Relative vertex asphericity
AU - Harlander, Jens
AU - Rosebrock, Stephan
N1 - Publisher Copyright:
©
PY - 2021/6
Y1 - 2021/6
N2 - 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 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.
AB - 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 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.
KW - AMS subject classification 57M20 20F05 20F06 20F65
UR - http://www.scopus.com/inward/record.url?scp=85086947821&partnerID=8YFLogxK
U2 - 10.4153/S0008439520000454
DO - 10.4153/S0008439520000454
M3 - Article
AN - SCOPUS:85086947821
SN - 0008-4395
VL - 64
SP - 292
EP - 305
JO - Canadian Mathematical Bulletin
JF - Canadian Mathematical Bulletin
IS - 2
ER -