Whitney towers and abelian invariants of knots

Cha, Jae Choon; Orr, Kent; Powell, Mark

Abstract

We relate certain abelian invariants of a knot, namely the Alexander polynomial, the Blanchfield form, and the Arf invariant, to intersection data of a Whitney tower in the 4-ball bounded by the knot. We also give a new 3-dimensional algorithm for computing these invariants.

Citation

Cha, J. C., Orr, K., & Powell, M. (2020). Whitney towers and abelian invariants of knots. Mathematische Zeitschrift, 294(1-2), 519-553. https://doi.org/10.1007/s00209-019-02293-x

• Journal Article Type: Article
• Acceptance Date: Feb 20, 2019
• Online Publication Date: Apr 5, 2019
• Publication Date: Feb 28, 2020
• Deposit Date: Mar 15, 2019
• Publicly Available Date: Apr 25, 2019
• Journal: Mathematische Zeitschrift
• Print ISSN: 0025-5874
• Electronic ISSN: 1432-1823
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 294
• Issue: 1-2
• Pages: 519-553
• DOI: https://doi.org/10.1007/s00209-019-02293-x
• Public URL: https://durham-repository.worktribe.com/output/1306045
• Related Public URLs: https://arxiv.org/abs/1606.03608