Concordance invariants from higher order covers

We generalize the Manolescu–Owens smooth concordance invariant δ ( K ) of knots K ⊂ S 3 to invariants δ p n ( K ) obtained by considering covers of order p n , with p a prime. Our main result shows that for any prime p ≠ 2 , the thus obtained homomorphism ⊕ n ∈ N δ p n 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.