论文标题
拉格朗日的恢复主义，lefschetz振动和量子不变性
Lagrangian cobordisms, Lefschetz fibrations and quantum invariants
论文作者
论文摘要
我们使用Lagrangian量子同源性提供的工具来研究拉格朗日的共同体。特别是，我们开发了在Lefschetz纤维化中设置具有圆柱末端的拉格朗日辅助主义或拉格朗日人的理论，并将量子同源组的不同版本置于长期的确切序列中。我们在这个长期的精确序列中证明了地图的各种实践关系，并提取不变性，将判别物的概念推广到lefschetz纤维中的拉格朗日恢复。我们证明了结果的结果与裁缝末端的判别物和恢复本身的关系。我们还举例说明了Lagrangian球体引起的例子，并将判别物与打开Gromov Witten的不变性相关联。我们表明，对于Lagrangian的某些配置，判别总是消失的。我们研究了一组示例，这些示例是由复杂的投影空间的复杂二次突出的lefschetz铅笔产生的。这些四边形是具有真实结构的象征性歧管，它们的真实部分是感兴趣的Lagrangians。利用本文中建立的结果，我们通过将计算减少到四遍中实际拉格朗日球体的先前确定的案例中来计算所有这些拉格朗日人的判别因素。
We study Lagrangian cobordisms with the tools provided by Lagrangian quantum homology. In particular, we develop the theory for the setting of Lagrangian cobordisms or Lagrangians with cylindrical ends in a Lefschetz fibration, and put the different versions of the quantum homology groups into relation by a long exact sequence. We prove various practical relations of maps in this long exact sequence and we extract invariants that generalize the notion of discriminants to Lagrangian cobordisms in Lefschetz fibrations. We prove results on the relation of the discriminants of the ends of a cobordism and the cobordism itself. We also give examples arising from Lagrangian spheres and relate the discriminant to open Gromov Witten invariants. We show that for some configurations of Lagrangian spheres the discriminant always vanishes. We study a set of examples that arise from Lefschetz pencils of complex quadric hypersurfaces of the complex projective space. These quadrics are symplectic manifolds endowed with real structures and their real part are the Lagrangians of interest. Using the results established in this thesis, we compute the discriminants of all these Lagrangians by reducing the calculation to the previously established case of a real Lagrangian sphere in the quadric.
