Homology concordance and knot Floer homology

We study the homology concordance group of knots in integer homology three-spheres which bound integer homology four-balls. Using knot Floer homology, we construct an infinite number of \(\mathbb {Z}\)-valued, linearly independent homology concordance homomorphisms which vanish for knots coming from \(S^3\). This shows that the homology concordance group modulo knots coming from \(S^3\) contains an infinite-rank summand. The techniques used here generalize the classification program established in previous papers regarding the local equivalence group of knot Floer complexes over \(\mathbb {F}[U, V]/(UV)\). Our results extend this approach to complexes defined over a broader class of rings.