Relative vertex asphericity

Jens Harlander; Stephan Rosebrock

doi:10.4153/S0008439520000454

Relative vertex asphericity

Jens Harlander
, Stephan Rosebrock

Mathematics Department

Karlsruhe University of Education

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 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.

Original language	English
Pages (from-to)	292-305
Number of pages	14
Journal	Canadian Mathematical Bulletin
Volume	64
Issue number	2
DOIs	https://doi.org/10.4153/S0008439520000454
State	Published - Jun 2021

Keywords

AMS subject classification 57M20 20F05 20F06 20F65

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10.4153/S0008439520000454

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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 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.",

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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 - https://www.scopus.com/pages/publications/85086947821

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 -

Relative vertex asphericity

Abstract

Keywords

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