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Holomorphic disks and knot invariants (2004)
| Venue: | Adv. in Math |
| Citations: | 184 - 22 self |
BibTeX
@INPROCEEDINGS{Ozsváth04holomorphicdisks,
author = {Peter Ozsváth and Zoltán Szabó},
title = {Holomorphic disks and knot invariants},
booktitle = {Adv. in Math},
year = {2004}
}
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Abstract
Abstract. We define a Floer-homology invariant for knots in an oriented threemanifold, closely related to the Heegaard Floer homologies for three-manifolds defined in [18]. 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 threemanifolds 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. 1.
