Applications of Heegaard Floer homology to knot and link concordance

We consider several applications of Heegaard Floer homology to the study of knot and link concordance.;We also present an algorithm for computing the knot Floer homology of the inverse image of a knot in its m-fold cyclic branched cover. Using this algorithm, as well as earlier work of Ozsvath and Szabo on the Floer homology of double branched covers, we determine the smooth concordance orders of numerous knots through eleven crossings.;Using the techniques of bordered Heegaard Floer homology developed recently by Lipshitz, Ozsvath, and Thurston, we compute the concordance invariant tau for a family of satellite knots that generalizes Whitehead doubles. We use this computation to show that the all-positive Whitehead doubles of certain links obtained by iterated Bing doubling are not smoothly slice.