Pseudoholomorphic curves and the symplectic isotopy problem

Abstract

The deformation problem for pseudoholomorphic curves and related geometrical properties of the total moduli space of pseudoholomorphic curves are studied. A sufficient condition for the saddle point property of the total moduli space is established. The local symplectic isotopy problem is formulated and solved for the case of imbedded pseudoholomorphic curves. It is shown that any two symplectically imbedded surfaces Sigma_0, Sigma_1 in CP^2 of the same degree d\le 6 are symplectically isotopic.

AMS-LaTeX, 94pages, 2 figures. The paper is submitted as the author's habilitation thesis at Ruhr-University, Bochum, Germany

References in corpus (2)

• The gluing construction for normally generic J-holomorphic curves
• Gromov compactness theorem for stable curves

Cited by in corpus (13)

• New obstructions to symplectic embeddings
• On Symplectic Sum Formulas in Gromov-Witten Theory
• A Comparison Theorem for Gromov-Witten Invariants in the Symplectic Category
• Automatic Transversality and Orbifolds of Punctured Holomorphic Curves in Dimension Four
• Moduli space of $J$-holomorphic subvarieties
• The Severi problem for Hirzebruch surfaces
• On the local version of the Severi problem
• Real Ruan-Tian Perturbations
• Intersection theoretic properties on the moduli space of genus 0 stable maps to a semipositive symplectic 4-manifold
• Courbes symplectiques de haute auto-intersection dans les surfaces symplectiques
• A four-dimensional mapping class group relation
• Counting real rational curves on real symplectic 4-manifolds with vanishing first Chern class
• Ruled 4-manifolds and isotopies of symplectic surfaces