Knot traces and concordance

Abstract

We give a method for constructing many pairs of distinct knots K 0 and K 1 such that the two 4-manifolds obtained by attaching a 2-handle to B 4 along K i with framing zero are diffeomorphic. We use the d-invariants of Heegaard Floer homology to obstruct the smooth concordance of some of these K 0 and K 1 , thereby disproving a conjecture of Abe. As a consequence, we obtain a proof that there exist patterns P in solid tori such that P ( K ) is not always concordant to P ( U ) # K and yet whose action on the smooth concordance group is invertible.