Geometry & Topology

Pseudoholomorphic punctured spheres in $\mathbb{R} \times (S^{1}\times S^{2})$: Moduli space parametrizations

Clifford Henry Taubes

Full-text: Open access

Abstract

This is the second of two articles that describe the moduli spaces of pseudoholomorphic, multiply punctured spheres in ×(S1×S2) as defined by a certain natural pair of almost complex structure and symplectic form. The first article in this series described the local structure of the moduli spaces and gave existence theorems. This article describes a stratification of the moduli spaces and gives explicit parametrizations for the various strata.

Article information

Source
Geom. Topol., Volume 10, Number 4 (2006), 1855-2054.

Dates
Received: 5 April 2005
Accepted: 25 October 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799796

Digital Object Identifier
doi:10.2140/gt.2006.10.1855

Mathematical Reviews number (MathSciNet)
MR2284051

Zentralblatt MATH identifier
1161.53075

Subjects
Primary: 53D30: Symplectic structures of moduli spaces
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53D05: Symplectic manifolds, general 57R17: Symplectic and contact topology

Keywords
pseudoholomorphic punctured sphere almost complex structure symplectic form moduli space

Citation

Taubes, Clifford Henry. Pseudoholomorphic punctured spheres in $\mathbb{R} \times (S^{1}\times S^{2})$: Moduli space parametrizations. Geom. Topol. 10 (2006), no. 4, 1855--2054. doi:10.2140/gt.2006.10.1855. https://projecteuclid.org/euclid.gt/1513799796


Export citation

References

  • F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003) 799–888
  • Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, GAFA 2000 (Tel Aviv, 1999), Geom. Funct. Anal. (2000) 560–673
  • D T Gay, R Kirby, Constructing symplectic forms on 4-manifolds which vanish on circles, Geom. Topol. 8 (2004) 743–777
  • H Hofer, Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. Math. 114 (1993) 515–563
  • H Hofer, Dynamics, topology, and holomorphic curves, from: “Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998)”, Extra Vol. I (1998) 255–280
  • H Hofer, Holomorphic curves and dynamics in dimension three, from: “Symplectic geometry and topology (Park City, UT, 1997)”, IAS/Park City Math. Ser. 7, Amer. Math. Soc., Providence, RI (1999) 35–101
  • H Hofer, K Wysocki, E Zehnder, Properties of pseudo-holomorphic curves in symplectisations. II. Embedding controls and algebraic invariants, Geom. Funct. Anal. 5 (1995) 270–328
  • 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
  • H Hofer, K Wysocki, E Zehnder, Properties of pseudoholomorphic curves in symplectizations. III. Fredholm theory, from: “Topics in nonlinear analysis. The Herbert Amman Anniversary”, Progr. Nonlinear Differential Equations Appl. 35, Birkhäuser, Basel (1999) 381–475
  • K Honda, An openness theorem for harmonic 2-forms on 4-manifolds, Illinois J. Math. 44 (2000) 479–495
  • D McDuff, The local behaviour of holomorphic curves in almost complex $4$-manifolds, J. Differential Geom. 34 (1991) 143–164
  • C H Taubes, The geometry of the Seiberg-Witten invariants, from: “Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998)”, Extra Vol. II (1998) 493–504
  • C H Taubes, Seiberg-Witten invariants, self-dual harmonic 2-forms and the Hofer-Wysocki-Zehnder formalism, from: “Surveys in differential geometry”, Surv. Differ. Geom., VII, Int. Press, Somerville, MA (2000) 625–672
  • C H Taubes, A compendium of pseudoholomorphic beasts in $\Bbb R\times (S\sp 1\times S\sp 2)$, Geom. Topol. 6 (2002) 657–814
  • C H Taubes, Pseudoholomorphic punctured spheres in $\Bbb R\times (S\sp 1\times S\sp 2)$: properties and existence, Geom. Topol. 10 (2006) 785–928