Decomposable braids as subgroups of braid groups
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- by H. Levinson PDF
- Trans. Amer. Math. Soc. 202 (1975), 51-55 Request permission
Abstract:
The group of all decomposable $3$-braids is the commutator subgroup of the group ${I_3}$ of all $3$-braids which leave strand positions invariant. The group of all $2$-decomposable $4$-braids is the commutator subgroup of ${I_4}$, and the group of all decomposable $4$-braids is explicitly characterized as a subgroup of the second commutator subgroup of ${I_4}$.References
- E. Artin, Theory of braids, Ann. of Math. (2) 48 (1947), 101–126. MR 19087, DOI 10.2307/1969218
- H. Levinson, Decomposable braids and linkages, Trans. Amer. Math. Soc. 178 (1973), 111–126. MR 324684, DOI 10.1090/S0002-9947-1973-0324684-X
- Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers [John Wiley & Sons], New York-London-Sydney, 1966. MR 0207802
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 202 (1975), 51-55
- MSC: Primary 55A25; Secondary 20F05
- DOI: https://doi.org/10.1090/S0002-9947-1975-0362287-3
- MathSciNet review: 0362287