Stability and isotopy of symplectomorphism groups of ruled surfaces
Jun Li (University of Michigan-Ann Arbor)
Abstract: The symplectomorphism groups $Symp(M, \omega)$ of ruled surfaces have been started by Gromov, McDuff, and Abreu, etc, using J-holomorphic techniques. For rational ruled surfaces, the topological structure of $Symp(M, \omega)$ is better understood, while for irrational cases our only knowledge is for minimal ruled surfaces. In this talk, we apply the J-inflation techniques of Anjos-Li-Li-Pinsonnault to irrational non-minimal ruled surfaces and prove a stability result for $Symp(M, \omega)$. As an application, we find symplectic mapping classes that are smoothly but not symplectically isotopic to identity. The talk is based on joint works with Olguta Buse.
algebraic geometrydifferential geometrysymplectic geometry
Audience: researchers in the topic
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Organizers: | Jose Mourao*, Rosa Sena Dias, SÃlvia Anjos* |
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