Tree groups and the 4-string pure braid group (Q803279)
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scientific article; zbMATH DE number 4200472
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Tree groups and the 4-string pure braid group |
scientific article; zbMATH DE number 4200472 |
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Tree groups and the 4-string pure braid group (English)
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1991
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It is shown that the (unperturbed) braid group on four strings \(B_ 4\) is an HNN-extension of the graph group \(F_ 5\) of a certain graph S having 5 vertices and 5 edges. As a consequence, a conjecture due to J. Tits, referring to the structure of a suitable subgroup of the braid group, is resolved for the special case \(B_ 4\). Various other results are obtained dealing for example with the question of the linearity of the braid groups.
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HNN-extension
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graph group
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braid groups
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