Isomorphisms in the Fukaya category of a Weinstein manifold with vanishing first Chern class automatically have trivial Whitehead torsion, so isomorphic Lagrangians are simple homotopy equivalent.
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Simple homotopy theory for Fukaya categories
Isomorphisms in the Fukaya category of a Weinstein manifold with vanishing first Chern class automatically have trivial Whitehead torsion, so isomorphic Lagrangians are simple homotopy equivalent.