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GTC: 2019 : Speaker: Boyu Zhang

Boyd Room 328

Title: Taut foliations and Seiberg-Witten invariants

Abstract: The question of existence and flexibility of taut foliations on a three-manifold has been studied for decades. Kronheimer, Mrowka, Ozsvath, and Szabo obtained Floer-theoretic obstructions for the existence of taut foliations on rational homology spheres by considering its perturbation to contact structures. By showing that the perturbed contact structure is unique in many cases, Vogel and Bowden constructed examples of taut foliations that are homotopic as distributions but cannot be deformed to each other through taut foliations. In this talk, we will propose a different approach. Instead of perturbing the foliation to a contact structure, we consider a symplectization of the foliation directly and use the Seiberg-Witten equations to define an invariant in Floer homology. We will then use this invariant to recover the obstruction of Kronheimer-Mrowka-Ozsvath-Szabo, and the non-flexibility result by Vogel and Bowden.

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