Whitehead torsion and Fukaya categories

The s-cobordism theorem uses simple homotopy equivalences, a refinement of homotopy equivalences detected by Whitehead torsion, to distinguish h-cobordant manifolds. More recently, it has appeared in symplectic geometry through the work of Abouzaid and Kragh, in connection with the topology of closed Lagrangian submanifolds of cotangent bundles. In this talk, I will present a categorical framework for simple homotopy theory in Fukaya categories, based on the fundamental group of the ambient symplectic manifold. This framework allows us to extend previous known results from cotangent bundles to general Weinstein manifolds.