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This is the second 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 this auxiliary manifold, its geometry and the relationship between the generators of the embedded contact homology chain complex and those of the Heegaard Floer chain complex. The pseudoholomorphic curves that define the differential on the embedded contact homology chain complex are also described here as a first step to relate the differential on the latter complex with that on the Heegaard Floer complex.
Kutluhan, Çağatay 1 ; Lee, Yi-Jen 2 ; Taubes, Clifford 3
@article{GT_2020_24_6_a5,
author = {Kutluhan, \c{C}a\u{g}atay and Lee, Yi-Jen and Taubes, Clifford},
title = {HF = {HM,} {II} : {Reeb} orbits and holomorphic curves for the {ech/Heegaard} {Floer} correspondence},
journal = {Geometry & topology},
pages = {2855--3012},
publisher = {mathdoc},
volume = {24},
number = {6},
year = {2020},
url = {http://geodesic.mathdoc.fr/item/GT_2020_24_6_a5/}
}
TY - JOUR AU - Kutluhan, Çağatay AU - Lee, Yi-Jen AU - Taubes, Clifford TI - HF = HM, II : Reeb orbits and holomorphic curves for the ech/Heegaard Floer correspondence JO - Geometry & topology PY - 2020 SP - 2855 EP - 3012 VL - 24 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/GT_2020_24_6_a5/ ID - GT_2020_24_6_a5 ER -
%0 Journal Article %A Kutluhan, Çağatay %A Lee, Yi-Jen %A Taubes, Clifford %T HF = HM, II : Reeb orbits and holomorphic curves for the ech/Heegaard Floer correspondence %J Geometry & topology %D 2020 %P 2855-3012 %V 24 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/GT_2020_24_6_a5/ %F GT_2020_24_6_a5
Kutluhan, Çağatay; Lee, Yi-Jen; Taubes, Clifford. HF = HM, II : Reeb orbits and holomorphic curves for the ech/Heegaard Floer correspondence. Geometry & topology, Tome 24 (2020) no. 6, pp. 2855-3012. http://geodesic.mathdoc.fr/item/GT_2020_24_6_a5/
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