Twisted Blanchfield pairings and twisted signatures III: Applications

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.

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