Homology concordance homomorphisms
Two knots in homology 3-spheres are homology concordant if they are smoothly concordant in a homology cobordism. I will explain how to construct integer-valued homomorphisms from this group of knots up to homology concordance. This construction generalizes concordance homomorphisms from knot Floer homology. This is joint work-in-progress with Irving Dai, Jen Hom, and Matt Stoffregen.