On sums of torus knots concordant to alternating knots

TL;DR

This paper investigates which sums of torus knots are concordant to alternating knots, focusing on sums of two torus knots and employing Heegaard Floer homology to develop effective obstructions.

Contribution

It introduces new obstructions based on Heegaard Floer homology for sums of two torus knots being concordant to alternating knots.

Findings

Obstructions derived from Heegaard Floer homology.

Analysis specific to sums of two torus knots.

Partial classification of concordance to alternating knots.

Abstract

We consider the question, asked by Friedl, Livingston and Zentner, of which sums of torus knots are concordant to alternating knots. After a brief analysis of the problem in its full generality, we focus on sums of two torus knots. We describe some effective obstructions based on Heegaard Floer homology.