Geometry & Topology

Embedded contact homology and Seiberg–Witten Floer cohomology III

Clifford Henry Taubes

Abstract

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.

Article information

Source
Geom. Topol., Volume 14, Number 5 (2010), 2721-2817.

Dates
Revised: 11 May 2010
Accepted: 1 June 2010
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732250

Digital Object Identifier
doi:10.2140/gt.2010.14.2721

Mathematical Reviews number (MathSciNet)
MR2746725

Zentralblatt MATH identifier
1276.57025

Citation

Taubes, Clifford Henry. Embedded contact homology and Seiberg–Witten Floer cohomology III. Geom. Topol. 14 (2010), no. 5, 2721--2817. doi:10.2140/gt.2010.14.2721. https://projecteuclid.org/euclid.gt/1513732250

References

• J-M Bismut, D S Freed, The analysis of elliptic families. I. Metrics and connections on determinant bundles, Comm. Math. Phys. 106 (1986) 159–176
• F Bourgeois, K Mohnke, Coherent orientations in symplectic field theory, Math. Z. 248 (2004) 123–146
• S K Donaldson, P B Kronheimer, The geometry of four-manifolds, Oxford Math. Monogr., Oxford Science Publ., The Clarendon Press, Oxford Univ. Press, New York (1990)
• R Gompf, private communication
• H Hofer, K Wysocki, E Zehnder, Properties of pseudoholomorphic curves in symplectisations. I. Asymptotics, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996) 337–379
• M Hutchings, An index inequality for embedded pseudoholomorphic curves in symplectizations, J. Eur. Math. Soc. $($JEMS$)$ 4 (2002) 313–361
• M Hutchings, C H Taubes, Gluing pseudoholomorphic curves along branched covered cylinders. I, J. Symplectic Geom. 5 (2007) 43–137
• M Hutchings, C H Taubes, Gluing pseudoholomorphic curves along branched covered cylinders. II, J. Symplectic Geom. 7 (2009) 29–133
• P Kronheimer, T Mrowka, Monopoles and three-manifolds, New Math. Monogr. 10, Cambridge Univ. Press (2007)
• T Mrowka, A local Mayer–Vietoris principle for Yang–Mills moduli spaces, PhD thesis, University of California, Berkeley (1989)
• D Quillen, Determinants of Cauchy–Riemann operators on Riemann surfaces, Funktsional. Anal. i Prilozhen. 19 (1985) 37–41, 96
• C H Taubes, Asymptotic spectral flow for Dirac operators, Comm. Anal. Geom. 15 (2007) 569–587
• \bibmarginparThe pages will be added when these are published. C H Taubes, Embedded contact homology and Seiberg–Witten Floer cohomology I, Geom. Topol. 14 (2010)
• \bibmarginparThe pages will be added when these are published. C H Taubes, Embedded contact homology and Seiberg–Witten Floer cohomology II, Geom. Topol. 14 (2010)
• C H Taubes, Embedded contact homology and Seiberg–Witten Floer cohomology IV, Geom. Topol. 14 (2010)