A note on knot concordance and involutive knot Floer homology

TL;DR

This paper establishes a relationship between knot concordance and involutive knot Floer complexes, showing that concordant knots have stably equivalent involutive Floer complexes, which advances understanding in knot theory and Floer homology.

Contribution

It introduces a new stable equivalence condition for involutive knot Floer complexes of concordant knots, providing a novel link between knot concordance and Floer homology.

Findings

Concordant knots have involutive Floer complexes satisfying a specific stable equivalence.

The result connects knot concordance with algebraic properties of Floer complexes.

Provides a new tool for studying knot concordance via Floer homology.

Abstract

We prove that if two knots are concordant, their involutive knot Floer complexes satisfy a certain type of stable equivalence.