Given a closed exact Lagrangian in the cotangent bundle of a closed smooth manifold, we prove that the projection to the base is a simple homotopy equivalence.
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We construct a hereditarily indecomposable Banach space with dual space isomorphic to$ℓ$_{1}. Every bounded linear operator on this space is expressible as λ$I$+$K$, with λ a scalar and$K$compact.