The Classification of fused links

Abstract

We construct the complete invariant for fused links. It is proved that the set of equivalence classes of $n$-component fused links is in one-to-one correspondence with the set of elements of the abelization $UV{P}_n/UV{P}_n^{\prime }$ up to conjugation by the elements from the symmetric group $S_n<UV{B}_n$.

48 pages, 11 figures