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Pseudoholomorphic curves in four-orbifolds and some applications

Weimin Chen
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Abstract

The main purpose of this paper is to summarize the basic ingredients, illustrated with examples, of a pseudoholomorphic curve theory for symplectic 4-orbifolds. These are extensions of relevant work of Gromov, McDuff and Taubes on symplectic 4-manifolds concerning pseudoholomorphic curves and Seiberg-Witten theory. They form the technical backbone of the proof that a symplectic s-cobordism of elliptic 3-manifolds (with a canonical contact structure on the boundary) is smoothly a product. One interesting feature of the theory is that existence of pseudoholomorphic curves gives certain restrictions on the singular points of the 4-orbifold contained by the pseudoholomorphic curves. In the last section, we discuss applications (or potential ones) of the theory in some other problems such as symplectic finite group actions on 4-manifolds, symplectic circle actions on 6-manifolds, and algebraic surfaces with quotient singularities.

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Weimin Chen. 2005-03-22. Pseudoholomorphic curves in four-orbifolds and some applications. https://arxiv.org/abs/math/0410608

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