Lagrangian spheres, symplectic surfaces and the symplectic mapping class group.

Wu, Weiwei
2012-07
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Lagrangian spheres, symplectic surfaces and the symplectic mapping class group.

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2012-07

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Given a Lagrangian sphere in a symplectic 4-manifold (M, &omega) with b=1, we find embedded symplectic surfaces intersecting it minimally. When the Kodaira dimension &kappa of (M, &omega) is -&infin, this minimal intersection property turns out to be very powerful for both the uniqueness and existence problems of Lagrangian spheres. On the uniqueness side, for a symplectic rational manifold and any class which is not characteristic, we show that homologous Lagrangian spheres are smoothly isotopic, and when the Euler number is less than 8, we generalize Hind and Evans' Hamiltonian uniqueness in the monotone case. On the existence side, when &kappa=-&infin, we give a characterization of classes represented by Lagrangian spheres, which enables us to describe the non-Torelli part of the symplectic mapping class group.

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University of Minnesota Ph.D. dissertation. July 2012. Major: Mathematics. Advisor: Tian-Jun Li. 1 computer file (PDF); iii, 61 pages.

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Wu, Weiwei. (2012). Lagrangian spheres, symplectic surfaces and the symplectic mapping class group.. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/135850.

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