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• W2158658835 abstract "We show how to measure the failure of the Whitney move in dimension 4 by constructing higher-order intersection invariants of Whitney towers built from iterated Whitney disks on immersed surfaces in 4-manifolds. For Whitney towers on immersed disks in the 4-ball, we identify some of these new invariants with previously known link invariants such as Milnor, Sato–Levine, and Arf invariants. We also define higher-order Sato–Levine and Arf invariants and show that these invariants detect the obstructions to framing a twisted Whitney tower. Together with Milnor invariants, these higher-order invariants are shown to classify the existence of (twisted) Whitney towers of increasing order in the 4-ball. A conjecture regarding the nontriviality of the higher-order Arf invariants is formulated, and related implications for filtrations of string links and 3-dimensional homology cylinders are described." @default.
• W2158658835 created "2016-06-24" @default.
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• W2158658835 date "2011-04-25" @default.
• W2158658835 modified "2023-09-23" @default.
• W2158658835 title "Higher-order intersections in low-dimensional topology" @default.
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• W2158658835 doi "https://doi.org/10.1073/pnas.1018581108" @default.
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