Constraints on Lefschetz fibrations with four-dimensional fibers

Abstract: I will describe constraints on the topology of Lefschetz fibrations with 4-dimensional fibers (in the smooth category), obtained from Seiberg-Witten theory. Our main result relates the index of a Dirac operator on the total space with the monodromy of the fibration, and is reminiscent of the Grothendieck-Riemann-Roch formula in the holomorphic setting. As topological applications, we construct closed simply-connected symplectic 4-manifolds which admit Torelli symplectic diffeomorphisms that are not isotopic to products of squared Dehn twists on Lagrangian spheres, answering a question of Donaldson in the negative. Based on joint work with Hokuto Konno, Jianfeng Lin, and Anubhav Mukherjee.

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic

Geometria em Lisboa (IST)

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