Real Algebraic and Analytic Geometry
Submission: 2008, May 6.
A differentiable manifold admits an algebraic model if it is diffeomorphic to some non-singular real algebraic set. We prove that every manifold whose underlying set is definable in some o-minimal structure admits an algebraic model, and the diffeomorphism can be chosen to be definable in this structure. For a large class of o-minimal expansions of the real exponential field, even definable smooth manifolds admit definably and smooth algebraic models.
Mathematics Subject Classification (2000): 14P05, 03C64, 32B20, 57D15, 58A07.
Keywords and Phrases: o-minimal structure, differentiable and smooth manifold, non-singular real algebraic set.
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