Embedded contact homology and Seiberg–Witten Floer cohomology V
Geometry & topology, Tome 14 (2010) no. 5, pp. 2961-3000.

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

This is a sequel to four earlier papers by the author that construct an isomorphism between the embedded contact homology and Seiberg–Witten Floer cohomology of a compact 3–manifold with a given contact 1–form. These respective homology/cohomology theories carry additional structure; this sequel proves that the isomorphism that is constructed in the first four papers is compatible with this extra structure.

DOI : 10.2140/gt.2010.14.2961
Keywords: Seiberg–Witten equations, Floer homology, contact homology

Taubes, Clifford Henry 1

1 Department of Mathematics, Harvard University, Cambridge, MA O2138, USA
@article{GT_2010_14_5_a4,
     author = {Taubes, Clifford Henry},
     title = {Embedded contact homology and {Seiberg{\textendash}Witten} {Floer} cohomology {V}},
     journal = {Geometry & topology},
     pages = {2961--3000},
     publisher = {mathdoc},
     volume = {14},
     number = {5},
     year = {2010},
     doi = {10.2140/gt.2010.14.2961},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2010.14.2961/}
}
TY  - JOUR
AU  - Taubes, Clifford Henry
TI  - Embedded contact homology and Seiberg–Witten Floer cohomology V
JO  - Geometry & topology
PY  - 2010
SP  - 2961
EP  - 3000
VL  - 14
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2010.14.2961/
DO  - 10.2140/gt.2010.14.2961
ID  - GT_2010_14_5_a4
ER  - 
%0 Journal Article
%A Taubes, Clifford Henry
%T Embedded contact homology and Seiberg–Witten Floer cohomology V
%J Geometry & topology
%D 2010
%P 2961-3000
%V 14
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2010.14.2961/
%R 10.2140/gt.2010.14.2961
%F GT_2010_14_5_a4
Taubes, Clifford Henry. Embedded contact homology and Seiberg–Witten Floer cohomology V. Geometry & topology, Tome 14 (2010) no. 5, pp. 2961-3000. doi : 10.2140/gt.2010.14.2961. http://geodesic.mathdoc.fr/articles/10.2140/gt.2010.14.2961/

[1] M Hutchings, An index inequality for embedded pseudoholomorphic curves in symplectizations, J. Eur. Math. Soc. $($JEMS$)$ 4 (2002) 313

[2] M Hutchings, 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

[3] M Hutchings, M Sullivan, Rounding corners of polygons and the embedded contact homology of $T^3$, Geom. Topol. 10 (2006) 169

[4] M Hutchings, C H Taubes, Gluing pseudoholomorphic curves along branched covered cylinders. I, J. Symplectic Geom. 5 (2007) 43

[5] M Hutchings, C H Taubes, The Weinstein conjecture for stable Hamiltonian structures, Geom. Topol. 13 (2009) 901

[6] P B Kronheimer, T S Mrowka, Monopoles and contact structures, Invent. Math. 130 (1997) 209

[7] P Kronheimer, T Mrowka, Monopoles and three-manifolds, New Math. Monographs 10, Cambridge Univ. Press (2007)

[8] C B Morrey Jr., Multiple integrals in the calculus of variations, Grund. der math. Wissenschaften 130, Springer (1966)

[9] C H Taubes, The Seiberg–Witten equations and the Weinstein conjecture. II. More closed integral curves of the Reeb vector field, Geom. Topol. 13 (2009) 1337

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

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

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

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

Cité par Sources :