Holomorphic disks and knot invariants

Peter Ozsvath; Zoltan Szabo

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Holomorphic disks and knot invariants

Peter Ozsvath·Zoltan Szabo

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Abstract

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 $S^3$, and also calculation of $HF^+$ for certain simple three-manifolds which fiber over the circle.

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BibTeX RIS

Peter Ozsvath, Zoltan Szabo. 2003-06-11. Holomorphic disks and knot invariants. https://arxiv.org/abs/math/0209056

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