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The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.
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Examples of Self-Maps of E8-Manifold
Let $M$ be a simply connected topological 4-manifold with intersection form given by the E8 lattice. Does anyone know of examples of continuous self-maps of $M$ of degree 2 or 3? Or of degree any ot …