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 →

During the Spring, I will be teaching a class on differential topology. Lecture Notes will not be posted on this blog since I will be explicitly using several books. The course will mainly be organized in two parts. Part 1. Introduction … Continue reading →