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

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

2001-09-19

arxiv.org/abs/math/0109134v1

Mathematics

Geometric Topology

17 pages, 11 figures

Scientific paper

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 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 invariants, or equivalently the Massey products.

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