Computing the rho-invariants of links via the signature of colored links with applications to the linear independence of twist knots

TL;DR

This paper extends the computation of rho-invariants from knots to links using Cimasoni-Florens' invariant, and applies it to prove the linear independence of certain twist knots in the concordance group.

Contribution

It generalizes rho-invariant computations to links and demonstrates the linear independence of twist knots with minimal exceptions.

Findings

Rho-invariants for links computed via Cimasoni-Florens invariant.

Twist knots of algebraic order two are mostly linearly independent in the concordance group.

Only twelve potential exceptions identified for the linear independence of these knots.

Abstract

We use a link invariant defined by Cimasoni-Florens to compute \rho-invariants. This generalizes results of Cochran-Teichner and Friedl on knots to the setting of links. As an application, we prove with only twelve possible exceptions that the twist knots of algebraic order two are linearly independent in the topological concordance group.