Milnor's Isotopy Invariants and Generalized Link Homotopy

Thomas Fleming; Akira Yasuhara

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arXiv · math/0511477

Milnor's Isotopy Invariants and Generalized Link Homotopy

Thomas Fleming·Akira Yasuhara

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Abstract

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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Thomas Fleming, Akira Yasuhara. 2005-11-21. Milnor's Isotopy Invariants and Generalized Link Homotopy. https://arxiv.org/abs/math/0511477

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