Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T13:10:28.747Z Has data issue: false hasContentIssue false
  • English
  • Français

Towards a characterization of smooth braids

Published online by Cambridge University Press:  24 October 2008

D. L. Johnson
D. L. Johnson
Affiliation:
University of Nottingham
Get access Rights & Permissions [Opens in a new window]

Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 3 , November 1982 , pp. 425 - 427
Copyright
Copyright © Cambridge Philosophical Society 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Chow, W.-L.On the algebraical braid group. Ann. of Math. (2) 49 (1948), 654–658.CrossRefGoogle Scholar
(2)JrHall, M.The theory of groups (Macmillan, New York, 1959).Google Scholar
(3)Johnson, D. L.Topics in the theory of group presentations (Cambridge University Press, 1980).CrossRefGoogle Scholar
(4)The Kourovka notebook of unsolved problems in group theory, 7th ed. (Novosibirsk, 1980).Google Scholar
(5)Markov, A. A.Foundations of the algebraic theory of braids. Trudy MIAN 16 (1945), 1–54.Google Scholar