Knot concordance invariants from Seiberg–Witten theory and slice genus bounds in 4-manifolds

We construct a new family of knot concordance invariants Formula: see text, where Formula: see text is a prime number. Our invariants are obtained from the equivariant Seiberg–Witten–Floer cohomology, constructed by the author and Hekmati, applied to the degree Formula: see text cyclic cover of Formula: see text branched over Formula: see text. In the case Formula: see text, our invariant Formula: see text shares many similarities with the knot Floer homology invariant Formula: see text defined by Hom and Wu. Our invariants Formula: see text give lower bounds on the genus of any smooth, properly embedded, homologically trivial surface bounding Formula: see text in a definite Formula: see text-manifold with boundary Formula: see text.