A generalized weight test with applications to tree presentations
type: Item
instance of: scholarly article
title: A generalized weight test with applications to tree presentations
zbMATH Open document ID: 0761.57003
DOI: 10.1007/BF02571435
author: Stephan Rosebrock
author: Günther Huck
published in: Mathematische Zeitschrift
publication date: 1993-03-03T00:00:00Z
full work available at URL: https://eudml.org/doc/174448
review text: We introduce the ``cycle test'', which is a generalization of Gersten's ``weight test'', to study diagrammatic reducibility of standard 2- complexes. Diagrammatic reducibility (DR) is a stronger combinatorial form of asphericity for 2-complexes. A homogeneous version of the cycle test leads to conditions that generalize small cancellation theory in its application as a test for DR; a fact which also has been observed by Gersten. Aside from that, the cycle test has many applications in a nonhomogeneous way, of which we present several examples. In particular, some of these examples are related to ``labelled oriented tree'' presentations whose 2-complexes are spines of ribbon disk complements.
Mathematics Subject Classification ID: 57M20
Mathematics Subject Classification ID: 20F06
Mathematics Subject Classification ID: 57M15
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 126404
zbMATH Keywords: labelled oriented tree
zbMATH Keywords: diagrammatic reducibility
zbMATH Keywords: standard 2-complexes
zbMATH Keywords: asphericity
zbMATH Keywords: cycle test
zbMATH Keywords: small cancellation
zbMATH Keywords: spines
zbMATH Keywords: ribbon disk
MaRDI profile type: Publication
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OpenAlex ID: W2086847115
description: scientific article; zbMATH DE number 126404