In this paper we study the interplay between Lagrangian cobordisms and stability conditions. We show that any stability condition on the derived Fukaya category $D\mathcal{F}uk(M)$ of a symplectic manifold $(M,\omega)$ induces a stability condition on the derived Fukaya category of Lagrangian cobordisms $D\mathcal{F}uk(\mathbb{C} \times M)$. We also discuss a relation between stability conditions and the Lagrangian cobordisms group. This provides a general framework in which Haug's result, that the Lagrangian cobordism group of $T^2$ is isomorphic to $K_0(D\mathcal{F}uk(T^2))$, can be understood.

中文翻译：

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稳定性条件和拉格朗日协边

在本文中，我们研究了拉格朗日协边和稳定性条件之间的相互作用。我们证明了辛流形 $(M,\omega)$ 的派生 Fukaya 范畴 $D\mathcal{F}uk(M)$ 上的任何稳定性条件都会在 Lagrangian cobordisms $D\ 的派生 Fukaya 范畴上引入稳定条件mathcal{F}uk(\mathbb{C} \times M)$。我们还讨论了稳定性条件和拉格朗日协边群之间的关系。这提供了一个通用框架，在该框架中可以理解 Haug 的结果，即 $T^2$ 的拉格朗日协边群与 $K_0(D\mathcal{F}uk(T^2))$ 同构。