Abstract
The group BSL(k) of boundary cobordism classes of boundary k-string links is defined. An epimorphism from BSL(k) to a group of cobordism classes of matrices is defined. An action of a certain group of pure braids on BSL(k) provides all possible splittings for a given boundary k-link. A necessary and sufficient condition is given for two elements of BSL(k) to have the same closure as an F(k)-link (i.e., a boundary k-link with one of its splittings), up to F(k)-cobordism.
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