Twisted Blanchfield pairings and twisted signatures III: Applications

Maciej Borodzik; Anthony Conway; Wojciech Politarczyk

Twisted Blanchfield pairings and twisted signatures III: Applications

Geometric Topology 2024-03-18 v2

Authors: Maciej Borodzik , Anthony Conway , Wojciech Politarczyk

Abstract

This paper describes how to compute algorithmically certain twisted signature invariants of a knot $K$ using twisted Blanchfield forms. An illustration of the algorithm is implemented on $(2,q)$ -torus knots. Additionally, using satellite formulas for these invariants, we also show how to obstruct the sliceness of certain iterated torus knots.

Keywords

twisted blanchfield form twisted signature invariant knot torus knot satellite formula sliceness

Cite

@article{arxiv.2111.10631,
  title  = {Twisted Blanchfield pairings and twisted signatures III: Applications},
  author = {Maciej Borodzik and Anthony Conway and Wojciech Politarczyk},
  journal= {arXiv preprint arXiv:2111.10631},
  year   = {2024}
}

Comments

35 pages, 4 figures. This is Section 9 of arXiv:1809.08791, which is now split into three papers: this is the third, the first is arxiv:2111.10632 and the second is arXiv:1809.08791. v2: Significant revision incorporating comments from a referee. Most notably Sections 5 and 6 are new. To appear in Glasgow Math. J

Twisted Blanchfield pairings and twisted signatures III: Applications

Abstract

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