Voir la notice de l'article provenant de la source Mathematical Sciences Publishers
This is the third of five papers that construct an isomorphism between the Seiberg–Witten Floer homology and the Heegaard Floer homology of a given compact, oriented –manifold. The isomorphism is given as a composition of three isomorphisms; the first of these relates a version of embedded contact homology on an auxiliary manifold to the Heegaard Floer homology on the original. This paper describes the relationship between the differential on the embedded contact homology chain complex and the differential on the Heegaard Floer chain complex. The paper also describes the relationship between the various canonical endomorphisms that act on the homology groups of these two complexes.
Kutluhan, Çağatay 1 ; Lee, Yi-Jen 2 ; Taubes, Clifford 3
@article{GT_2020_24_6_a6,
author = {Kutluhan, \c{C}a\u{g}atay and Lee, Yi-Jen and Taubes, Clifford},
title = {HF = {HM,} {III} : {Holomorphic} curves and the differential for the {ech/Heegaard} {Floer} correspondence},
journal = {Geometry & topology},
pages = {3013--3218},
publisher = {mathdoc},
volume = {24},
number = {6},
year = {2020},
url = {http://geodesic.mathdoc.fr/item/GT_2020_24_6_a6/}
}
TY - JOUR AU - Kutluhan, Çağatay AU - Lee, Yi-Jen AU - Taubes, Clifford TI - HF = HM, III : Holomorphic curves and the differential for the ech/Heegaard Floer correspondence JO - Geometry & topology PY - 2020 SP - 3013 EP - 3218 VL - 24 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/GT_2020_24_6_a6/ ID - GT_2020_24_6_a6 ER -
%0 Journal Article %A Kutluhan, Çağatay %A Lee, Yi-Jen %A Taubes, Clifford %T HF = HM, III : Holomorphic curves and the differential for the ech/Heegaard Floer correspondence %J Geometry & topology %D 2020 %P 3013-3218 %V 24 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/GT_2020_24_6_a6/ %F GT_2020_24_6_a6
Kutluhan, Çağatay; Lee, Yi-Jen; Taubes, Clifford. HF = HM, III : Holomorphic curves and the differential for the ech/Heegaard Floer correspondence. Geometry & topology, Tome 24 (2020) no. 6, pp. 3013-3218. http://geodesic.mathdoc.fr/item/GT_2020_24_6_a6/
[1] , Morrey spaces, Springer (2015) | DOI
[2] , Complex analysis: an introduction to the theory of analytic functions of one complex variable, McGraw-Hill (1978)
[3] , , , Properties of pseudoholomorphic curves in symplectisations, I : Asymptotics, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996) 337 | DOI
[4] , The embedded contact homology index revisited, from: "New perspectives and challenges in symplectic field theory" (editors M Abreu, F Lalonde, L Polterovich), CRM Proc. Lecture Notes 49, Amer. Math. Soc. (2009) 263
[5] , 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] , , Rounding corners of polygons and the embedded contact homology of T3, Geom. Topol. 10 (2006) 169 | DOI
[7] , , Gluing pseudoholomorphic curves along branched covered cylinders, II, J. Symplectic Geom. 7 (2009) 29 | DOI
[8] , , , HF = HM, I : Heegaard Floer homology and Seiberg–Witten Floer homology, Geom. Topol. 24 (2020) 2829 | DOI
[9] , , , HF = HM, II : Reeb orbits and holomorphic curves for the ech/Heegaard Floer correspondence, Geom. Topol. 24 (2020) 2855 | DOI
[10] , A cylindrical reformulation of Heegaard Floer homology, Geom. Topol. 10 (2006) 955 | DOI
[11] , , J–holomorphic curves and quantum cohomology, 6, Amer. Math. Soc. (1994) | DOI
[12] , Multiple integrals in the calculus of variations, 130, Springer (1966) | DOI
[13] , , Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. 159 (2004) 1027 | DOI
[14] , , An introduction to Heegaard Floer homology, from: "Floer homology, gauge theory, and low-dimensional topology" (editors D A Ellwood, P S Ozsváth, A I Stipsicz, Z Szabó), Clay Math. Proc. 5, Amer. Math. Soc. (2006) 3
[15] , Determinants of Cauchy–Riemann operators on Riemann surfaces, Funktsional. Anal. i Prilozhen. 19 (1985) 37
[16] , , , Morrey–Campanato spaces : an overview, from: "Operator theory, pseudo-differential equations, and mathematical physics" (editors Y I Karlovich, L Rodino, B Silbermann, I M Spitkovsky), Oper. Theory Adv. Appl. 228, Springer (2013) 293 | DOI
[17] , Floer homology and knot complements, PhD thesis, Harvard University (2003)
[18] , Relative asymptotic behavior of pseudoholomorphic half-cylinders, Comm. Pure Appl. Math. 61 (2008) 1631 | DOI
[19] , SW ⇒ Gr : from the Seiberg–Witten equations to pseudo-holomorphic curves, J. Amer. Math. Soc. 9 (1996) 845 | DOI
[20] , A compendium of pseudoholomorphic beasts in R × (S1 × S2), Geom. Topol. 6 (2002) 657 | DOI