More concordance homomorphisms from knot Floer homology

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 $\mathbb{𝔽}\left[U,V\right]∕\left(UV=0\right)$. 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.