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Category Archives: Differential Topology
Solve Exercises 10,14,15,16,18,19 in Chapter 1 of the book “The Laplacian on a Riemannian manifold”.
John Milnor is a renowned mathematician who made fundamental contributions to differential topology and was awarded the Fields medal in 1962. One of his most striking result is the existence of several distinct differentiable structures on the 7 dimensional sphere (!). The following … Continue reading
Exercise 1. Show that the sphere is a -dimensional smooth manifold. Exercise 2. We consider the following two subsets of the plane and . Are and smooth manifolds ? Of course, justify your answer with a proof. Exercise 3. Let be a n-dimensional … Continue reading