Abstract Given an exact symplectic manifold M and a support Lagrangian Λ ⊂ M , we construct an ∞-category Lag Λ ( M ) which we conjecture to be equivalent (after specialization of the coefficients) to the partially wrapped Fukaya category of M relative to Λ. Roughly speaking, the objects of Lag Λ ( M ) are Lagrangian branes inside of M × T ⁎ R n , for large n, and the morphisms are Lagrangian cobordisms that are non-characteristic with respect to Λ. The main theorem of this paper is that Lag Λ ( M ) is a stable ∞-category, and in particular its homotopy category is triangulated, with mapping cones given by an elementary construction. The shift functor is equivalent to the familiar shift of grading for Lagrangian branes.

中文翻译：

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一个稳定的 ∞ 类拉格朗日协边

摘要 给定一个精确的辛流形 M 和一个支持拉格朗日 Λ ⊂ M ，我们构造了一个 ∞ 类别 Lag Λ ( M )，我们推测它是等价的（在系数特化后）M 相对于 Λ 的部分包裹的 Fukaya 类别. 粗略地说，Lag Λ ( M ) 的对象是 M × T ⁎ R n 内部的拉格朗日膜，对于大 n，态射是关于 Λ 的非特征的拉格朗日协边。本文的主要定理是 Lag Λ ( M ) 是一个稳定的 ∞ 范畴，特别是它的同伦范畴是三角剖分的，映射锥由一个初等构造给出。移位函子相当于我们熟悉的拉格朗日膜分级移位。