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Holomorphic disks and knot invariants

2003; Elsevier BV; Volume: 186; Issue: 1 Linguagem: Inglês

10.1016/j.aim.2003.05.001

1090-2082

Peter Ozsváth, Zoltán Szabó,

semigroups and automata theory

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.