Holomorphic disks and knot invariants

We define a Floer-homology invariant for knots in an oriented three-manifold, closely related to the Heegaard Floer homologies for three-manifolds defined in an earlier paper. We set up basic properties of these invariants, including an Euler characteristic calculation, and a description of the behavior under connected sums. Then, we establish a relationship with HF⁺ for surgeries along the knot. Applications include calculation of HF⁺ of three-manifolds obtained by surgeries on some special knots in S³, and also calculation of HF⁺ for certain simple three-manifolds which fiber over the circle.