*The primary source is the seminal 1963 differential-topology article, "Groups of homotopy spheres," by Michel Kervaire and John Milnor.*

In the last lecture, we got as far as setting up a spectral sequence. This is to show the vanishing of the rational homology groups of the fiber F of the map S^m --> K(Z,m). Today, we will do the calculation.

(This will finish Serre's argument that the stable homotopy groups of spheres are finite, for positive indices. This fact is used by Kervaire--Milnor in their showing that the groups of homotopy spheres are finite.)

Afterward, time permitting, Professor Khan will review the construction of the Leray--Serre spectral sequence that was used.