Twisted Blanchfield pairings and twisted signatures III: Applications

TL;DR

This paper develops an algorithm to compute twisted signature invariants of knots using twisted Blanchfield forms, demonstrating applications to obstructing sliceness of iterated torus knots.

Contribution

It introduces an algorithmic method for calculating twisted signature invariants and applies satellite formulas to obstruct sliceness of complex knots.

Findings

Algorithm successfully computes invariants for (2,q)-torus knots.

Satellite formulas help obstruct sliceness of certain iterated torus knots.

Implementation demonstrates practical computation of twisted signatures.

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.