Concordance invariants from higher order covers

We generalize the Manolescu–Owens smooth concordance invariant δ(K) of knots K⊂S3 to invariants δpn(K) obtained by considering covers of order pn, with p a prime. Our main result shows that for any prime p≠2, the thus obtained homomorphism ⊕n∈Nδpn from the smooth concordance group to Z∞ has infinite rank. We also show that unlike δ, these new invariants typically are not multiples of the knot signature, even for alternating knots. A significant portion of the article is devoted to exploring examples.