# More concordance homomorphisms from knot Floer homology

## TL;DR

This paper introduces a new infinite family of smooth concordance homomorphisms derived from knot Floer homology, which are explicitly computable and have applications in knot concordance and related invariants.

## Contribution

It defines an infinite family of linearly independent, integer-valued concordance homomorphisms based on local equivalence classes of knot Floer complexes.

## Key findings

- The homomorphisms are explicitly computable.
- They provide new insights into topologically slice knots.
- Applications include bounds on concordance genus and unknotting number.

## Abstract

We define an infinite family of linearly independent, integer-valued smooth concordance homomorphisms. Our homomorphisms are explicitly computable and rely on local equivalence classes of knot Floer complexes over the ring $\mathbb{F}[U, V]/(UV=0)$. We compare our invariants to other concordance homomorphisms coming from knot Floer homology, and discuss applications to topologically slice knots, concordance genus, and concordance unknotting number.