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Towards a characterization of smooth braids

  • D. L. Johnson (a1)
Abstract

The braid group on n + 1 strings has the presentation

where xi corresponds to the single crossing of the i string over the i + 1 string, and rij is a commutator when i < j − 1, and a braid relator when i = j − 1. B1 is the trivial group and B2 is infinite cyclic; we shall assume n ≥ 2 throughout.

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References
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(1) W.-L. Chow On the algebraical braid group. Ann. of Math. (2) 49 (1948), 654658.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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