Whitney tower concordance of classical links
The authors continue their analyses of Whitney towers of Whitney disks. Some earlier work which this 60 page paper reiterates, elaborates, strengthens and generalizes may be found for example in: [\textit{J. Conant, R. Schneiderman} and \textit{P. Teichner}, Compos. Math. 143, No. 3, 780--810 (2007; Zbl 1128.57004), and Geom. Topol. 16, No. 1, 555--600 (2012; Zbl 1284.57007)], also \textit{R. Schneiderman} [Trans. Am. Math. Soc. 358, No. 10, 4251--4278 (2006; Zbl 1117.57021)] and \textit{R. Schneiderman} and \textit{P. Teichner} [Geometry and Topology Monographs 7, 101--134 (2004; Zbl 1090.57013)].NEWLINENEWLINEThe (framed and graded) Whitney tower here is generalized to allow twisted disks of order at least 1/2 the order of the tower. The resulting filtration of the tower is specialized to those which arise from framed links in \(S^3\). The theory developed allows determination of an obstruction to a link bounding an order \(n\) Whitney tower. Careful study of this obstruction invariant leads to the following conclusion: A link bounds an order \(n\) Whitney tower in the 4-ball if and only if the Milnor link invariants, higher order Sato-Levine invariants and higher order Arf invariants vanish up to order \(n\).NEWLINENEWLINEThe authors display and verify the commutativity of two formidable diagrams which summarize much of the paper's work.NEWLINENEWLINEA characterization of Milnor's invariants is also presented.
scientific article; zbMATH DE number 6068630
scientific article