The effect of mutation on link concordance, 3-manifolds, and the Milnor invariants

Abstract

We study the effect of mutation on link concordance and 3-manifolds. We show that the set of links concordant to sublinks of homology boundary links is not closed under positive mutation. We also show that mutation does not preserve homology cobordism classes of 3-manifolds. A significant consequence is that there exist 3-manifolds which have the same quantum SU(2) -invariants but are not homology cobordant. These results are obtained by investigating the effect of mutation on the Milnor (mu) over bar -invariants, or equivalently the Massey products.