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arxiv: 1904.05137 · v1 · pith:BNQW6DXLnew · submitted 2019-04-10 · 🧮 math.GT

Symplectic surfaces and bridge position

classification 🧮 math.GT
keywords symplecticbridgesurfacesurfacesisotopicpositionproofsmoothly
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We give a new characterization of symplectic surfaces in CP^2 via bridge trisections. Specifically, a minimal genus surface in CP^2 is smoothly isotopic to a symplectic surface if and only if it is smoothly isotopic to a surface in transverse bridge position. We discuss several potential applications, including the classification of unit 2-knots, establishing the triviality of Gluck twists, the symplectic isotopy problem, Auroux's proof that every symplectic 4-manifold is a branched cover over CP^2, and the existence of Weinstein trisections. The proof exploits a well-known connection between symplectic surfaces and quasipositive factorizations of the full twist in the braid group.

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