Milnor's Isotopy Invariants and Generalized Link Homotopy

2005/11/21 by Thomas Fleming, Fleming, Thomas, Akira Yasuhara +1
Mathematics · #57M25 (Primary) 57M27 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25 #msc:57M27

paper · pdf · doi:10.48550/arxiv.math/0511477

7 pages, 5 figures (low resolution)

arxiv created 2005/11/21 · arxiv updated 2009/12/01

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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