Article
The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions II
Publications Mathématiques de l'IHÉS, Tome 139 (2024), pp. 189-348

This paper is the sequel to (Colin et al. in Publ. Math. Inst. Hautes Études Sci., 2024), and is devoted to proving some of the technical parts of the HF=ECH isomorphism.

Reçu le :
Accepté le :
Première publication :
Publié le :
DOI : 10.1007/s10240-024-00146-w
@article{PMIHES_2024__139__189_0,
     author = {Colin, Vincent and Ghiggini, Paolo and Honda, Ko},
     title = {The equivalence of {Heegaard} {Floer} homology and embedded contact homology via open book decompositions {II}},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {189--348},
     year = {2024},
     publisher = {Springer International Publishing},
     address = {Cham},
     volume = {139},
     doi = {10.1007/s10240-024-00146-w},
     mrnumber = {4750570},
     zbl = {1557.57018},
     language = {en},
     url = {https://www.numdam.org/articles/10.1007/s10240-024-00146-w/}
}
TY  - JOUR
AU  - Colin, Vincent
AU  - Ghiggini, Paolo
AU  - Honda, Ko
TI  - The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions II
JO  - Publications Mathématiques de l'IHÉS
PY  - 2024
SP  - 189
EP  - 348
VL  - 139
PB  - Springer International Publishing
PP  - Cham
UR  - https://www.numdam.org/articles/10.1007/s10240-024-00146-w/
DO  - 10.1007/s10240-024-00146-w
LA  - en
ID  - PMIHES_2024__139__189_0
ER  - 
%0 Journal Article
%A Colin, Vincent
%A Ghiggini, Paolo
%A Honda, Ko
%T The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions II
%J Publications Mathématiques de l'IHÉS
%D 2024
%P 189-348
%V 139
%I Springer International Publishing
%C Cham
%U https://www.numdam.org/articles/10.1007/s10240-024-00146-w/
%R 10.1007/s10240-024-00146-w
%G en
%F PMIHES_2024__139__189_0
Colin, Vincent; Ghiggini, Paolo; Honda, Ko. The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions II. Publications Mathématiques de l'IHÉS, Tome 139 (2024), pp. 189-348. doi: 10.1007/s10240-024-00146-w

[0.] V. Colin, P. Ghiggini and K. Honda, Embedded contact homology and open book decompositions, Geom. Topol., to appear.

[I.] V. Colin, P. Ghiggini and K. Honda, The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions I, Publ. Math. Inst. Hautes Études Sci., (2024). | DOI | MR

[II.] V. Colin, P. Ghiggini and K. Honda, The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions II, Publ. Math. Inst. Hautes Études Sci., (2024), this paper. | DOI | MR

[III.] V. Colin, P. Ghiggini and K. Honda, The equivalence of Heegaard Floer homology and embedded contact homology III: from hat to plus, Publ. Math. Inst. Hautes Études Sci., (2024). | DOI | MR

[BH.] Bao, E.; Honda, K. Definition of cylindrical contact homology in dimension three, J. Topol., Volume 11 (2018), pp. 1001-1052 | MR | Zbl | DOI

[Bo1.] Bourgeois, F. A Morse Bott approach to contact homology, from: “Symplectic and contact topology: interactions and perspectives, Fields Inst. Comm., 35, Am. Math. Soc., Providence, 2003, pp. 55-77 | MR | Zbl

[Bo2.] F. Bourgeois, A Morse-Bott approach to contact homology, Ph.D. Thesis, 2002. | MR

[BEHWZ.] Bourgeois, F.; Eliashberg, Y.; Hofer, H.; Wysocki, K.; Zehnder, E. Compactness results in symplectic field theory, Geom. Topol., Volume 7 (2003), pp. 799-888 | MR | DOI | Zbl

[EES.] Etnyre, J.; Ekholm, T.; Sullivan, M. The contact homology of Legendrian submanifolds in 𝐑 2n+1 , J. Differ. Geom., Volume 71 (2005), pp. 177-305 | MR | Zbl

[Gr.] Gromov, M. Pseudo holomorphic curves in symplectic manifolds, Invent. Math., Volume 82 (1985), pp. 307-347 | MR | Zbl | DOI

[HLS.] Hofer, H.; Lizan, V.; Sikorav, J.-C. On genericity for holomorphic curves in four-dimensional almost complex manifolds, J. Geom. Anal., Volume 7 (1997), pp. 149-159 | MR | DOI | Zbl

[HWZ1.] Hofer, H.; Wysocki, K.; Zehnder, E. Properties of pseudoholomorphic curves in symplectisations. I. Asymptotics, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 13 (1996), pp. 337-379 | MR | DOI | Zbl | Numdam

[Hör.] Hörmander, L. The analysis of linear partial differential operators I, Springer, Berlin, 1990, p. xii+440 pp. (ISBN: 3-540-52343-X) | MR | Zbl

[HKM.] K. Honda, W. Kazez and G. Matić, Contact structures, sutured Floer homology, and TQFT, preprint (2008), | arXiv

[Hu1.] Hutchings, M. An index inequality for embedded pseudoholomorphic curves in symplectizations, J. Eur. Math. Soc., Volume 4 (2002), pp. 313-361 | MR | DOI | Zbl

[Hu2.] Hutchings, M. The embedded contact homology index revisited, New perspectives and challenges in symplectic field theory, CRM Proc. Lecture Notes, 49, Am. Math. Soc., Providence, 2009, pp. 263-297 | MR | Zbl | DOI

[HT1.] Hutchings, M.; Taubes, C. Gluing pseudoholomorphic curves along branched covered cylinders I, J. Symplectic Geom., Volume 5 (2007), pp. 43-137 | MR | DOI | Zbl

[HT2.] Hutchings, M.; Taubes, C. Gluing pseudoholomorphic curves along branched covered cylinders II, J. Symplectic Geom., Volume 7 (2009), pp. 29-133 | MR | Zbl | DOI

[HT3.] Hutchings, M.; Taubes, C. Proof of the Arnold chord conjecture in three dimensions 1, Math. Res. Lett., Volume 18 (2011), pp. 295-313 | MR | Zbl | DOI

[IP1.] Ionel, E.; Parker, T. Relative Gromov-Witten invariants, Ann. Math. (2), Volume 157 (2003), pp. 45-96 | MR | Zbl | DOI

[IP2.] Ionel, E.; Parker, T. The symplectic sum formula for Gromov-Witten invariants, Ann. Math. (2), Volume 159 (2004), pp. 935-1025 | MR | Zbl | DOI

[IS.] S. Ivashkovich and V. Shevchishin, Gromov compactness theorem for J-complex curves with boundary, Int. Math. Res. Not. (2000), 1167–1206. | MR

[LR.] Li, A.; Ruan, Y. Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds, Invent. Math., Volume 145 (2001), pp. 151-218 | MR | Zbl | DOI

[Li.] Lipshitz, R. A cylindrical reformulation of Heegaard Floer homology, Geom. Topol., Volume 10 (2006), pp. 955-1097 | MR | DOI | Zbl

[M.] D. McDuff, Comparing absolute and relative Gromov-Witten invariants, preprint (2008).

[MS.] McDuff, D.; Salamon, D. J -holomorphic curves and symplectic topology, 52, Am. Math. Soc., Providence, 2004 | MR | Zbl

[Pa.] Parker, B. Exploded fibrations, Proceedings of Gökova Geometry-Topology Conference 2006, 52–90, Gökova Geometry/Topology Conference (GGT), 2007, pp. 52-90 (Gökova) | MR | Zbl

[Se.] Seidel, P. A long exact sequence for symplectic Floer cohomology, Topology, Volume 42 (2003), pp. 1003-1063 | MR | DOI | Zbl

[We1.] C. Wendl, Finite energy foliations and surgery on transverse links, Ph.D. Thesis, 2005. | MR

[We2.] Wendl, C. Automatic transversality and orbifolds of punctured holomorphic curves in dimension four, Comment. Math. Helv., Volume 85 (2010), pp. 347-407 | MR | Zbl | DOI

Cité par Sources :