Title: Stability Conditions and Lagrangian Cobordisms,
Abstract: 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 $D\mathcal{F}uk(\mathbb{C} \times M)$. In addition, using stability
conditions, we provide general conditions under which the homomorphism $\Theta:
\Omega_{Lag}(M)\to K_0(D\mathcal{F}uk(M))$, introduced by Biran and Cornea, is
an isomorphism. This yields a better understanding of how stability conditions
affect $\Theta$ and it allows us to elucidate Haug's result, that the
Lagrangian cobordism group of $T^2$ is isomorphic to
$K_0(D\mathcal{F}uk(T^2))$.