Decomposable braids and linkages
Henry W. Levinson · Transactions of the American Mathematical Society · 1973
An n -braid is called k -decomposable if and only if the removal of k arbitrary strands results in a trivial ( n − k ) (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.