Geodesic
HF = HM, I : Heegaard Floer homology and Seiberg–Witten Floer homology
Kutluhan, Çağatay1 ; Lee, Yi-Jen2 ; Taubes, Clifford3
1 Department of Mathematics, University at Buffalo, Buffalo, NY, United States
2 Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
3 Department of Mathematics, Harvard University, Cambridge, MA, United States
Geometry & topology, Tome 24 (2020) no. 6, pp. 2829-2854.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

Let M be a closed, connected and oriented 3–manifold. This article is the first of a five-part series that constructs an isomorphism between the Heegaard Floer homology groups of M and the corresponding Seiberg–Witten Floer homology groups of M.

Classification : 53C07, 53C15
Keywords: Heegaard Floer homology, Seiberg–Witten Floer homology

Kutluhan, Çağatay 1 ; Lee, Yi-Jen 2 ; Taubes, Clifford 3

1 Department of Mathematics, University at Buffalo, Buffalo, NY, United States
2 Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
3 Department of Mathematics, Harvard University, Cambridge, MA, United States 
@article{GT_2020_24_6_a4,
     author = {Kutluhan, \c{C}a\u{g}atay and Lee, Yi-Jen and Taubes, Clifford},
     title = {HF = {HM,} {I} : {Heegaard} {Floer} homology and {Seiberg{\textendash}Witten} {Floer} homology},
     journal = {Geometry & topology},
     pages = {2829--2854},
     publisher = {mathdoc},
     volume = {24},
     number = {6},
     year = {2020},
     url = {http://geodesic.mathdoc.fr/item/GT_2020_24_6_a4/}
}
TY  - JOUR
AU  - Kutluhan, Çağatay
AU  - Lee, Yi-Jen
AU  - Taubes, Clifford
TI  - HF = HM, I : Heegaard Floer homology and Seiberg–Witten Floer homology
JO  - Geometry & topology
PY  - 2020
SP  - 2829
EP  - 2854
VL  - 24
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/GT_2020_24_6_a4/
ID  - GT_2020_24_6_a4
ER  - 
%0 Journal Article
%A Kutluhan, Çağatay
%A Lee, Yi-Jen
%A Taubes, Clifford
%T HF = HM, I : Heegaard Floer homology and Seiberg–Witten Floer homology
%J Geometry & topology
%D 2020
%P 2829-2854
%V 24
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/GT_2020_24_6_a4/
%F GT_2020_24_6_a4
Kutluhan, Çağatay; Lee, Yi-Jen; Taubes, Clifford. HF = HM, I : Heegaard Floer homology and Seiberg–Witten Floer homology. Geometry & topology, Tome 24 (2020) no. 6, pp. 2829-2854. http://geodesic.mathdoc.fr/item/GT_2020_24_6_a4/

[1] V Colin, P Ghiggini, K Honda, Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions, Proc. Natl. Acad. Sci. USA 108 (2011) 8100 | DOI

[2] V Colin, P Ghiggini, K Honda, The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions, I, preprint (2012)

[3] V Colin, P Ghiggini, K Honda, The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions, II, preprint (2012)

[4] V Colin, P Ghiggini, K Honda, The equivalence of Heegaard Floer homology and embedded contact homology, III: From hat to plus, preprint (2012)

[5] M Hutchings, Embedded contact homology and its applications, from: "Proceedings of the International Congress of Mathematicians" (editors R Bhatia, A Pal, G Rangarajan, V Srinivas, M Vanninathan, P Gastesi), Hindustan Book Agency (2010) 1022

[6] M Hutchings, M Sullivan, The periodic Floer homology of a Dehn twist, Algebr. Geom. Topol. 5 (2005) 301 | DOI

[7] M Hutchings, M Sullivan, Rounding corners of polygons and the embedded contact homology of T3, Geom. Topol. 10 (2006) 169 | DOI

[8] J D S Jones, Cyclic homology and equivariant homology, Invent. Math. 87 (1987) 403 | DOI

[9] P B Kronheimer, C Manolescu, Periodic Floer pro-spectra from the Seiberg–Witten equations, preprint (2002)

[10] P Kronheimer, T Mrowka, Monopoles and three-manifolds, 10, Cambridge Univ. Press (2007) | DOI

[11] Ç Kutluhan, Y J Lee, C H Taubes, HF = HM, II : Reeb orbits and holomorphic curves for the ech/Heegaard–Floer correspondence, Geom. Topol. 24 (2020) 2855 | DOI

[12] Ç Kutluhan, Y J Lee, C H Taubes, HF = HM, III : Holomorphic curves and the differential for the ech/Heegaard Floer correspondence, Geom. Topol. 24 (2020) 3013 | DOI

[13] Ç Kutluhan, Y J Lee, C H Taubes, HF = HM, IV : The Seiberg–Witten Floer homology and ech correspondence, Geom. Topol. 24 (2020) 3219 | DOI

[14] Ç Kutluhan, Y J Lee, C H Taubes, HF = HM, V : Seiberg–Witten–Floer homology and handle addition, Geom. Topol. 24 (2020) 3471 | DOI

[15] Y J Lee, Heegaard splittings and Seiberg–Witten monopoles, from: "Geometry and topology of manifolds" (editors H U Boden, I Hambleton, A J Nicas, B D Park), Fields Inst. Commun. 47, Amer. Math. Soc. (2005) 173

[16] Y J Lee, C H Taubes, Periodic Floer homology and Seiberg–Witten–Floer cohomology, J. Symplectic Geom. 10 (2012) 81 | DOI

[17] R Lipshitz, A cylindrical reformulation of Heegaard Floer homology, Geom. Topol. 10 (2006) 955 | DOI

[18] P Ozsváth, Z Szabó, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. 159 (2004) 1159 | DOI

[19] P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. 159 (2004) 1027 | DOI

[20] C H Taubes, Embedded contact homology and Seiberg–Witten Floer cohomology, I, Geom. Topol. 14 (2010) 2497 | DOI

[21] C H Taubes, Embedded contact homology and Seiberg–Witten Floer cohomology, II, Geom. Topol. 14 (2010) 2583 | DOI

[22] C H Taubes, Embedded contact homology and Seiberg–Witten Floer cohomology, III, Geom. Topol. 14 (2010) 2721 | DOI

[23] C H Taubes, Embedded contact homology and Seiberg–Witten Floer cohomology, IV, Geom. Topol. 14 (2010) 2819 | DOI

[24] C H Taubes, Embedded contact homology and Seiberg–Witten Floer cohomology, V, Geom. Topol. 14 (2010) 2961 | DOI