Milnor Invariants and Twisted Whitney Towers

Mathematics – Geometric Topology

Scientific paper

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Reworked exposition, updated figures and references. Minor edits and typos corrected

Scientific paper

This paper describes the relationship between the first non-vanishing Milnor invariants of a link in the 3-sphere and the tree-valued intersection invariant of a twisted Whitney tower in the 4-ball bounded by the link. This relationship plays a key role in the classifications of both the framed and twisted Whitney tower filtrations on link concordance, and here the higher-order Arf invariants associated to these filtrations are shown to detect the difference between two natural notions of `nilpotent approximations' to slicing a link. Also described are new geometric characterizations of links with vanishing Milnor invariants of length less than or equal to 2k.

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