ALGEBRAIC MODELS FOR O-MINIMAL MANIFOLDS
A difierentiable manifold admits an algebraic model if it is difieo- morphic to some non-singular real algebraic set. We prove that every manifold whose underlying set is deflnable in some o-minimal structure admits an al- gebraic model, and the difieomorphism can be chosen to be deflnable in this structure. For a large class of o-minimal expansions of the real exponential fleld, even deflnable smooth manifolds admit deflnably and smooth algebraic models.