Article thumbnail

Higher-order intersections in low-dimensional topology

By Jim Conant, Rob Schneiderman and Peter Teichner

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

Topics: Low Dimensional Geometry and Topology Special Feature
Publisher: National Academy of Sciences
OAI identifier: oai:pubmedcentral.nih.gov:3100959
Provided by: PubMed Central
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://www.pubmedcentral.nih.g... (external link)

  • To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.

    Suggested articles