Milnor's Isotopy Invariants and Generalized Link Homotopy

Details Milnor's Isotopy Invariants and Generalized Link Homotopy Milnor's Isotopy Invariants and Generalized Link Homotopy

2005-11-21

arxiv.org/abs/math/0511477v1

Mathematics

Geometric Topology

7 pages, 5 figures (low resolution)

Scientific paper

It has long been known that a Milnor invariant with no repeated index is an
invariant of link homotopy. We show that Milnor's invariants with repeated
indices are invariants not only of isotopy, but also of self C_k-moves. A self
C_k-move is a natural generalization of link homotopy based on certain degree k
clasper surgeries, which provides a filtration of link homotopy classes.

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