Embedded contact homology and Seiberg–Witten Floer cohomology III

Taubes, Clifford Henry¹

¹ Department of Mathematics, Harvard University, Cambridge, MA 02138, USA

Geometry & topology, Tome 14 (2010) no. 5, pp. 2721-2817.

Résumé

This is the third of five papers 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.

Détail

DOI : 10.2140/gt.2010.14.2721

Keywords: Seiberg–Witten equations, Floer homology, contact homology

Bibliographie

[1] J M Bismut, D S Freed, The analysis of elliptic families. I. Metrics and connections on determinant bundles, Comm. Math. Phys. 106 (1986) 159

[2] F Bourgeois, K Mohnke, Coherent orientations in symplectic field theory, Math. Z. 248 (2004) 123

[3] S K Donaldson, P B Kronheimer, The geometry of four-manifolds, Oxford Math. Monogr., Oxford Science Publ., The Clarendon Press, Oxford Univ. Press (1990)

[4] R Gompf, private communication

[5] H Hofer, K Wysocki, E Zehnder, Properties of pseudoholomorphic curves in symplectisations. I. Asymptotics, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996) 337

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

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

[8] M Hutchings, C H Taubes, Gluing pseudoholomorphic curves along branched covered cylinders. II, J. Symplectic Geom. 7 (2009) 29

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

[10] T Mrowka, A local Mayer–Vietoris principle for Yang–Mills moduli spaces, PhD thesis, University of California, Berkeley (1989)

[11] D Quillen, Determinants of Cauchy–Riemann operators on Riemann surfaces, Funktsional. Anal. i Prilozhen. 19 (1985) 37, 96

[12] C H Taubes, Asymptotic spectral flow for Dirac operators, Comm. Anal. Geom. 15 (2007) 569

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

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

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