Introduction to the basics of Heegaard Floer homology
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 22 (2013) no. 2, p. 269-336

This paper provides an introduction to the basics of Heegaard Floer homology with some emphasis on the hat theory and to the contact geometric invariants in the theory. The exposition is designed to be comprehensible to people without any prior knowledge of the subject.

Nous présentons une introduction aux éléments de la théorie d’Heegaard Floer et aux invariants qui proviennent d’une structure de contact. La présentation ne présuppose aucune connaissance du sujet.

@article{AFST_2013_6_22_2_269_0,
     author = {Sahamie, Bijan},
     title = {Introduction to the basics of Heegaard Floer homology},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 22},
     number = {2},
     year = {2013},
     pages = {269-336},
     doi = {10.5802/afst.1373},
     zbl = {1270.57048},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2013_6_22_2_269_0}
}
Sahamie, Bijan. Introduction to the basics of Heegaard Floer homology. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 22 (2013) no. 2, pp. 269-336. doi : 10.5802/afst.1373. http://www.numdam.org/item/AFST_2013_6_22_2_269_0/

[1] Bredon (G. E.).— Geometry and Topology, Graduate Texts in Mathematics 139, Springer-Verlag (1993). | MR 1224675 | Zbl 0791.55001

[2] Ding (F.) and Geiges (H.).— Symplectic fillability of tight contact structures on torus bundles, Algebr. Geom. Topol. 1, p. 153-172 (2001). | MR 1823497 | Zbl 0974.53061

[3] Ding (F.) and Geiges (H.).— A Legendrian surgery presentation of contact 3-manifolds, Math. Proc. Cambridge Philos. Soc. 136, p. 583-598 (2004). | MR 2055048 | Zbl 1069.57015

[4] Eliashberg (Y.).— Topological characterization of Stein manifolds of dimension >2, Internat. J. Math. 1, p. 29-46. | MR 1044658 | Zbl 0699.58002

[5] Etnyre (J. B.).— Lectures on open-book decompositions and contact structures, Amer. Math. Soc. 5, p. 103-142, (Proceedings of the Clay Mathematics Summer School) (2006). | MR 2249250 | Zbl 1108.53050

[6] Geiges (H.).— An Introduction to Contact Topology, Cambridge Studies in Advanced Mathematics 109, Cambridge University Press (2008). | MR 2397738 | Zbl 1153.53002

[7] Gompf (R. E.) and Stipsicz (A. I.).— 4-Manifolds and Kirby Calculus, Graduate Studies in Mathematics 20, American Mathematical Society (1999). | MR 1707327 | Zbl 0933.57020

[8] Honda (K.), Kazez (W. H.), and Matić (G.).— On the contact class in Heegaard Floer homology, J. Diff. Geom. 83(2), p. 289-311 (2009). | MR 2577470 | Zbl 1186.53098

[9] Lipshitz (R.), Ozsváth (P.) and Thurston (D.).— Bordered Heegaard Floer homology: Invariance and pairing, arXiv:0810.0687.

[10] Lisca (P.), Ozsváth (P.), Stipsicz (A. I.) and Szabó (Z.).— Heegaard Floer invariants of Legendrian knots in contact three-manifolds, J. Eur. Math. Soc (JEMS) 11(6), p. 1307-1363 (2009). | MR 2557137 | Zbl 1232.57017

[11] McDuff (D.) and Salamon (D.).— j-Holomorphic Curves and Symplectic Topology, Colloquium Publications 52, American Mathematical Society (2004). | MR 2045629 | Zbl 1064.53051

[12] Juhasz (A.).— Holomorphic disks and sutured manifolds, Algebr. Geom. Topol. 6, p. 1429-1457 (2006). | MR 2253454 | Zbl 1129.57039

[13] Ozsváth (P.) and Stipsicz (A. I.).— Contact surgeries and the transverse invariant in knot Floer homology, J. Inst. Math. Jussieu bf 9(3) (2010), 601-632. | MR 2650809 | Zbl 1204.57011

[14] Ozsváth (P.) and Szabó (Z.).— Holomorphic disks and knot invariants, Adv. Math. 186(1), p. 58-116 (2004). | MR 2065507 | Zbl 1062.57019

[15] Ozsváth (P.) and Szabó (Z.).— Heegaard Floer homologies and contact structures, Duke Math. J. 129(1), p. 39-61 (2005). | MR 2153455 | Zbl 1083.57042

[16] Ozsváth (P.) and Szabó (Z.).— Heegaard diagrams and holomorphic disks, Diff. faces of Geom., Int. Math. Series p. 301-348. | MR 2102999 | Zbl 1091.57010

[17] Ozsváth (P.) and Szabó (Z.).— Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. 159(3), p. 1027-1158 (2004). | MR 2113019 | Zbl 1073.57009

[18] Ozsváth (P.) and Szabó (Z.).— Holomorphic disks and three-manifold invariants: Properties and applications, Ann. of Math. 159(3), p. 1159-1245 (2004). | MR 2113020 | Zbl 1081.57013

[19] Ozsváth (P.) and Szabó (Z.).— Holomorphic triangles and invariants of smooth four-manifolds, Adv. Math. 202(2), p. 326-400 (2006). | MR 2222356 | Zbl 1099.53058

[20] Ozsváth (P.) and Szabó (Z.).— On the Heegaard Floer homology of branched double-covers, Adv. Math. 194, p. 1-33 (2005). | MR 2141852 | Zbl 1076.57013

[21] Ozsváth (P.) and Szabó (Z.).— Introduction to Heegaard Floer theory, Clay Math. Proc. 5, p. 3-28 (2006). | Zbl 1107.57022

[22] Ozsváth (P.) and Szabó (Z.).— Lectures on Heegaard Floer homology, Clay Math. Proc. 5, p. 29-70 (2006). | MR 2249248 | Zbl 1105.57029

[23] Ozsváth (P.) and Szabó (Z.).— Heegaard diagrams and holomorphic disks, Different faces of geometry p. 301-348. | MR 2102999 | Zbl 1091.57010

[24] Ozsváth (P.) and Szabó (Z.).— On the skein exact sequence for knot Floer homology, arXiv:0707.1165.

[25] Ozbagci (B.) and Stipsicz (A. I.).— Surgery on Contact 3-Manifolds and Stein Surfaces, Bolyai Society Mathematical Studies 13, Springer-Verlag (2004). | MR 2114165 | Zbl 1067.57024

[26] Sahamie (B.).— Dehn twists in Heegaard Floer homology, Algebr. Geom. Topol. 10, p. 465-524 (2010). | MR 2602843 | Zbl 1209.57017

[27] Sarkar (S.) and Wang (J.).— An algorithm for computing some Heegaard Floer homologies, Ann. of Math., vol. 171 (2), p. 1213-1236 (2010). | MR 2630063 | Zbl 1228.57017

[28] Turaev (V.).— Torsion invariants of Spin c -structures on 3-manifolds, Math. Research Letters 6, p. 679-695 (1997). | MR 1484699 | Zbl 0891.57019