Adding a suitable unknot to any link equates bridge number and meridional rank
Abstract
Given any link L⊂eq S3, we show that it is possible to embed an unknot U in its complement so that the link L U satisfies the Meridional Rank Conjecture (MRC). The bridge numbers in our construction fit into the equality β(L U)=2β(L)-1=rank(π1(S3 (L U))). In addition, we prove the MRC for new infinite families of links and distinguish them from previously settled cases through an application of bridge distance.
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