English

Signature invariants related to the unknotting number

Geometric Topology 2020-03-18 v2

Abstract

New lower bounds on the unknotting number of a knot are constructed from the classical knot signature function. These bounds can be twice as strong as previously known signature bounds. They can also be stronger than known bounds arising from Heegaard Floer and Khovanov homology. Results include new bounds on the Gordian distance between knots and information about four-dimensional knot invariants. By considering a related non-balanced signature function, bounds on the unknotting number of slice knots are constructed; these are related to the property of double-sliceness.

Keywords

Cite

@article{arxiv.1710.10530,
  title  = {Signature invariants related to the unknotting number},
  author = {Charles Livingston},
  journal= {arXiv preprint arXiv:1710.10530},
  year   = {2020}
}

Comments

13 pages, 3 figures. Added results concern signature bounds on the unknotting number of slice knots