A general small cancellation theory (Q2703071)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A general small cancellation theory |
scientific article |
Statements
19 November 2001
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small cancellation theory
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CW complexes
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Cayley complexes
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categories
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van Kampen lemma
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hyperbolic groups
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Dehn's algorithm
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presentations
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word problem
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conjugacy problem
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automorphism groups
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A general small cancellation theory (English)
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In this article a generalized version of small cancellation theory is developed which is applicable to specific types of high-dimensional simplicial complexes. It is shown that many results about small cancellation groups are true also in this new setting.NEWLINENEWLINENEWLINEThe main results are summarized in Theorem A. If \(G=\langle A\mid R\rangle\) is a general small cancellation presentation with \(\alpha\leq 1/12\), then the word and conjugacy problems for \(G\) are decidable, the Cayley graph is constructible, the Cayley category of the presentation is contractible, and \(G\) is the direct limit of hyperbolic groups. If in addition, the presentation satisfies some additional hypotheses, then every finite subgroup of \(G\) is a subgroup of the automorphism group of some general relator in \(R\).
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