title: Higher-order intersections in low-dimensional topology.
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.
authors.affiliation: Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, USA.
authors.forename: Jim
authors.initials: J
authors.lastname: Conant
authors.forename: Rob
authors.initials: R
authors.lastname: Schneiderman
authors.forename: Peter
authors.initials: P
authors.lastname: Teichner