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Relative vertex asphericity

Part of: Low-dimensional topology Special aspects of infinite or finite groups

Published online by Cambridge University Press:  16 June 2020

Jens Harlander  and
Stephan Rosebrock
Jens Harlander
Affiliation:
Department of Mathematics, Boise State University, Boise, ID83725-1555, USA e-mail: jensharlander@boisestate.edu
Stephan Rosebrock*
Affiliation:
Pädagogische Hochschule Karlsruhe, Bismarckstr. 10, 76133Karlsruhe, Germany
*
e-mail: rosebrock@ph-karlsruhe.de
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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 $(L,K)$ , 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.

Keywords

Diagrammatic reducibilityasphericity2-complexweight testrelative asphericity

MSC classification

Primary: 57M20: Two-dimensional complexes
Secondary: 20F05: Generators, relations, and presentations 20F06: Cancellation theory; application of van Kampen diagrams 20F65: Geometric group theory
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 2 , June 2021 , pp. 292 - 305
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Copyright
© Canadian Mathematical Society 2020

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