On knots with infinite smooth concordance order

TL;DR

This paper applies Heegaard Floer obstructions to determine the concordance order of knots, showing that most knots with previously unknown order actually have infinite concordance order.

Contribution

It demonstrates the effectiveness of Heegaard Floer obstructions in classifying the concordance order of knots up to eleven crossings.

Findings

46 out of 67 knots have infinite concordance order

Heegaard Floer obstructions are a powerful tool for knot concordance classification

Most knots with unknown order are shown to have infinite order

Abstract

We use the Heegaard Floer obstructions defined by Grigsby, Ruberman, and Strle to show that forty-six of the sixty-seven knots through eleven crossings whose concordance orders were previously unknown have infinite concordance order.