On Seiberg-Witten equationsοn symplectic 4-manifolds

Klaus Mohnke

Banach Center Publications (1997)

  • Volume: 39, Issue: 1, page 89-104
  • ISSN: 0137-6934

Abstract

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We discuss Taubes' idea to perturb the monopole equations on symplectic manifolds to compute the Seiberg-Witten invariants in the light of Witten's symmetry trick in the Kähler case.

How to cite

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Mohnke, Klaus. "On Seiberg-Witten equationsοn symplectic 4-manifolds." Banach Center Publications 39.1 (1997): 89-104. <http://eudml.org/doc/208682>.

@article{Mohnke1997,
abstract = {We discuss Taubes' idea to perturb the monopole equations on symplectic manifolds to compute the Seiberg-Witten invariants in the light of Witten's symmetry trick in the Kähler case.},
author = {Mohnke, Klaus},
journal = {Banach Center Publications},
keywords = {symplectic structures; monopole equations; Seiberg-Witten invariants},
language = {eng},
number = {1},
pages = {89-104},
title = {On Seiberg-Witten equationsοn symplectic 4-manifolds},
url = {http://eudml.org/doc/208682},
volume = {39},
year = {1997},
}

TY - JOUR
AU - Mohnke, Klaus
TI - On Seiberg-Witten equationsοn symplectic 4-manifolds
JO - Banach Center Publications
PY - 1997
VL - 39
IS - 1
SP - 89
EP - 104
AB - We discuss Taubes' idea to perturb the monopole equations on symplectic manifolds to compute the Seiberg-Witten invariants in the light of Witten's symmetry trick in the Kähler case.
LA - eng
KW - symplectic structures; monopole equations; Seiberg-Witten invariants
UR - http://eudml.org/doc/208682
ER -

References

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  1. [A] M. Audin, Exemples de variétés presque complexes, Enseign. Math. (2) 37 (1991), 175-190. Zbl0736.53036
  2. [BGV] N. Berline, E. Getzler, M. Vergne, Heat Kernels and the Dirac Operators, Grundlehren der Mathematischen Wissenschaften, Springer 1991. 
  3. [FM] R. Friedman, J. W. Morgan, Algebraic surfaces and Seiberg-Witten invariants, alg-geom/9502026, 1995. 
  4. [F] Th. Friedrich, Neue Invarianten der 4-dimensionalen Mannigfaltigkeiten, SFB 288-Preprint 156, 1995. 
  5. [G] M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347. Zbl0592.53025
  6. [KM] P. B. Kronheimer, T. S. Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Lett. 1 (1994), 797-808. Zbl0851.57023
  7. [LB] C. LeBrun, Einstein Metrics and Mostow Rigidity, Math. Res. Lett. 2 (1995), 1-8. 
  8. [D] D. McDuff, Rational and ruled symplectic 4-manifolds and Erratum, J. Amer. Math. Soc. 3 (1992), 988-997. Zbl0799.53039
  9. [T] C. H. Taubes, The Seiberg-Witten Invariants and Symplectic Forms, Math. Res. Lett. 1 (1994), 809-822. Zbl0853.57019
  10. [T1] C. H. Taubes, More Constraints on Symplectic Forms from Seiberg-Witten Invariants, Math. Res. Lett. 2 (1995), 9-14. Zbl0854.57019
  11. [T2] C. H. Taubes, The Seiberg-Witten and the Gromov invariants, Math. Res. Lett. 2 (1995), 221-238. Zbl0854.57020
  12. [W] E. Witten, Monopoles and 4-Manifolds, Math. Res. Lett. 1 (1994), 769-796. Zbl0867.57029

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