A rho-invariant of iterated torus knots

TL;DR

This paper calculates the rho-invariant for iterated torus knots using the abelianized representation, revealing a strong connection to algebraic geometry invariants of plane curve singularities.

Contribution

It introduces a method to compute the rho-invariant for iterated torus knots and links it to algebraic geometry invariants of singularities.

Findings

Rho-invariant computed explicitly for iterated torus knots

Connection established between rho-invariant and plane curve singularity invariants

Results applicable to algebraic knots and their geometric properties

Abstract

We compute rho-invariant for iterated torus knots $K$ for the standard representation of the knot group given by abelianisation. For algebraic knots, this invariant turns out to be very closely related to an invariant of a plane curve singularity, coming from algebraic geometry.