Ordering pure braid groups on compact, connected surfaces. (Q700685)
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scientific article; zbMATH DE number 1818971
| Language | Label | Description | Also known as |
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| English | Ordering pure braid groups on compact, connected surfaces. |
scientific article; zbMATH DE number 1818971 |
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Ordering pure braid groups on compact, connected surfaces. (English)
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22 October 2002
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The following main results are obtained: 1) If \(M\) is a closed orientable surface, then the pure braid group \(PB_n(M)\) is orderable (Theorem 1.6); 2) If \(M\) is a closed, non-orientable surface, then the pure braid group \(PB_n(M)\) has generalized torsion, for \(n\geq 2\). Therefore, \(PB_n(M)\) is not orderable for \(n\geq 2\) (Theorem 1.7).
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ordered braid groups
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pure braid groups
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surfaces
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generalized torsion
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