Decomposable braids and linkages
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- by H. Levinson PDF
- Trans. Amer. Math. Soc. 178 (1973), 111-126 Request permission
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
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J. W. Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. U.S.A. 9 (1923), 93-95.
- E. Artin, Theory of braids, Ann. of Math. (2) 48 (1947), 101–126. MR 19087, DOI 10.2307/1969218
- Wilhelm Magnus and Ada Peluso, On knot groups, Comm. Pure Appl. Math. 20 (1967), 749–770. MR 222880, DOI 10.1002/cpa.3160200407
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 178 (1973), 111-126
- MSC: Primary 55A25; Secondary 57C45
- DOI: https://doi.org/10.1090/S0002-9947-1973-0324684-X
- MathSciNet review: 0324684