Semesterside for MAT4520 - Vår 2010

The last two lectures will be Wednesday May 19. and Thursday May 27. The lectures Thursday May 20. and Wednesday 26. are cancelled. Note that the exam will be June 7. and June 8.

19. mai 2010 13:39

The final version of the supplementary notes has now been posted.

12. mai 2010 12:50

I have followed Spivak rather closely until page 265, but after this I do things differently. After giving a somewhat different proof of Corollary 8, p.266, I proved the homotopy invariance of de Rham cohomology (Theorem 13, p.277) and jumped to chapter 11 and construction of the Mayer-Vietoris sequence. As an illustration I calculated the cohomology of spheres and presented two applications: Brouwer's fixed point theorem and the proof that a sphere admits a nonsingular vector field if and only if the dimension is odd. In the remaining time I will continue to study de Rham cohomology. Most of the results will be found in Spivak's book, but the treatment will differ in some places. Supplementary notes will be found here.

2. mai 2010 18:51