中科院数学与系统科学研究院
数学研究所
学术报告
拓扑研讨班
报告人：Fabio Gironella ( 南特大学 )
题 目：Vanishing cycles for symplectic foliations
时 间：2024.05.15（星期三）10:00-11:00
地 点：数学院南楼N402
摘 要：The main objects of the talk will be symplectic foliations, and more precisely a subclass of these called "strong". Strong symplectic foliations are meant to be one of the possible rigid generalizations of taut foliations to high dimensions, and indeed have quite a rigid nature, with techniques such as pseudo-holomorphic curves à la Gromov and asymptotically holomorphic sequences of sections à la Donaldson working well in this setting. I will present a joint work in progress with Klaus Niederkrüger and Lauran Toussaint that aims at giving a new obstruction for a symplectic foliation to be strong. This comes in the form of a symplectic high-dimensional version of vanishing cycles for smooth codimension 1 foliations on 3-manifolds, and the proof relies on pseudo-holomorphic curve techniques, in a way which is parallel to the case of the Plastikstufe introduced by Niederkrüger '06 in the contact case.
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