Linear independence of rationally slice knots

TL;DR

This paper constructs an infinite family of rationally slice knots that are linearly independent in the knot concordance group, demonstrating they all have infinite order, unlike previously known examples.

Contribution

It introduces a new infinite family of rationally slice knots with infinite order, expanding understanding of their algebraic properties in knot concordance.

Findings

Constructed an infinite family of rationally slice knots.

Proved these knots are linearly independent in the concordance group.

Showed all examples have infinite order, unlike previous order-two examples.

Abstract

A knot in $S^3$ is rationally slice if it bounds a disk in a rational homology ball. We give an infinite family of rationally slice knots that are linearly independent in the knot concordance group. In particular, our examples are all infinite order. All previously known examples of rationally slice knots were order two.