Projective twists and the Hopf correspondence
Brunella Torricelli (Cambridge)
Monday 13th May, 2019 16:00-17:00 Maths 311B
Ever since Seidel's early work on Dehn twists around Lagrangian spheres, this class of symplectomorphisms has gained the attention of the symplectic community. In particular, these maps have supplied insightful examples of nontrivial symplectomorphisms that are not detectable by the smooth structure. The study of symplectic mapping class groups through the lens of Dehn twists and the relations they satisfy has become an active and fruitful area of research in symplectic topology. Little is known about the role of the projective counterparts of Dehn twists (around Lagrangian projective spaces), the so-called projective twists, within the symplectic mapping class group.
In this talk I will explain how to use results of Keating and Barth-Geiges-Zehmish established for Dehn twists to infer new information about projective twists. In the cases I consider, (the functors induced by) these symplectomorphisms are related to each other by an appropriate Lagrangian correspondence (in the setting of Mau-Woodward-Wehrheim theory). In particular, we obtain a free generation result for two projective twists along the core components of a plumbing of projective spaces, and a milder statement for a more general setting in certain Liouville manifolds.