Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Decomposable braids and linkages

Author: H. Levinson
Journal: Trans. Amer. Math. Soc. 178 (1973), 111-126
MSC: Primary 55A25; Secondary 57C45
MathSciNet review: 0324684
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An n-braid is called k-decomposable if and only if the removal of k arbitrary strands results in a trivial $ (n - k)$-braid. k-decomposable n-linkages are similarly defined. All k-decomposable n-braids are generated by an explicit geometric process, and so are all k-decomposable n-linkages. The latter are not always closures of k-decomposable n-braids. Many examples are given.

References [Enhancements On Off] (What's this?)

  • [1] J. W. Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. U.S.A. 9 (1923), 93-95.
  • [2] E. Artin, Theory of braids, Ann. of Math. (2) 48 (1947), 101-126. MR 8, 367. MR 0019087 (8:367a)
  • [3] W. Magnus and A. Peluso, On knot groups, Comm. Pure Appl. Math. 20 (1967), 749-770. MR 36 #5930. MR 0222880 (36:5930)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55A25, 57C45

Retrieve articles in all journals with MSC: 55A25, 57C45

Additional Information

Keywords: Decomposable, braids, linkages, groups
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society