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 [Formula: see text]-invariants, or equivalently the Massey products.
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