论文标题
扭曲的生成功能和附近的拉格朗日猜想
Twisted generating functions and the nearby Lagrangian conjecture
论文作者
论文摘要
我们证明，对于Cotangent束的封闭封闭的精确嵌入的拉格朗日submanifolds，稳定的Lagrangian Gauss映射诱导的同型组的同态同态消失。特别是，我们证明该地图对于所有球体都是无效的。我们引入的关键工具是为了证明这是扭曲生成函数的概念，我们证明，可以使用这种对象来描述每个封闭的精确拉格朗日式，通过扩展在保湿理论的设置中开发的加倍参数。浮子理论和捆绑理论限制了与Waldhausen的管子空间密切相关的类扭曲生成函数的类型，我们的主要结果遵循Bökstedt的定理，该定理计算了管子的合理同型类型。
We prove that, for closed exact embedded Lagrangian submanifolds of cotangent bundles, the homomorphism of homotopy groups induced by the stable Lagrangian Gauss map vanishes. In particular, we prove that this map is null-homotopic for all spheres. The key tool that we introduce in order to prove this is the notion of twisted generating function and we show that every closed exact Lagrangian can be described using such an object, by extending a doubling argument developed in the setting of sheaf theory. Floer theory and sheaf theory constrain the type of twisted generating functions that can appear to a class which is closely related to Waldhausen's tube space, and our main result follows by a theorem of Bökstedt which computes the rational homotopy type of the tube space.
