Differential topology

In the previous post we studied some “easy” cases of homotopy groups of spheres. We focused most on the group $\pi_3(S^2)$ and its computation from the Hopf fibration. All groups calculated last time were part of the so-called unstable range, meaning that they are not invariant under suspension. Due to the Freudenthal suspension theorem we know precicely the stable range for homotopy groups of spheres, and these are given by the stable homotopy groups....

For those that don’t know I am a fifth year mathematics student at NTNU, meaning I am finishing my masters degree after this semester. During my time at NTNU I have had some wonderful classes, and some wonderful teachers. Since most I post about on this blog is related to topology, it is very safe to assume that some of my most memorable courses are exactly the topology courses. I very recently looked at my notes from my first topology course, or rather one of the two first, as I took two in parallel during my fourth semester....