# Connected Floer homology of covering involutions

## TL;DR

This paper introduces new knot invariants derived from the covering involution on double branched covers, leading to new results on the linear independence of knots in the smooth concordance group.

## Contribution

It adapts existing ideas to define novel invariants from covering involutions, advancing understanding of knot concordance.

## Key findings

- New knot invariants from covering involutions
- Linear independence results in smooth concordance group
- Application of adapted ideas to knot theory

## Abstract

Using the covering involution on the double branched cover of the three-sphere branched along a knot, and adapting ideas of Hendricks-Manolescu and Hendricks-Hom-Lidman, we define new knot invariants and apply them to deduce novel linear independence results in the smooth concordance group of knots.