2002/09/30 by Peter Ozsvath, Zoltan Szabo · 3 citations
Mathematics · #math.GT #math.SG
published as Adv. Math. 186 (2004), no. 1, 58--116. · 64 pages, 17. Revised version
arxiv created 2003/06/11 · arxiv updated 2009/11/30
We define a Floer-homology invariant for knots in an oriented three-manifold, closely related to the holomorphic disk Floer homologies for three-manifolds defined in an earlier paper. We set up basic properties of these invariants, including an Euler characteristic calculation, behaviour 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.