Abstract: In this talk, we will see how we can obtain a formula to compute the equivariant cohomology of a $G$-manifold $M$ for $G$ a group in terms of the equivariant cohomology of the fixed points $F$ of the $G$-actions. This formula depends on the equivariant Euler class of the normal bundle of the fixed points and both the push forward and pull back of the inclusion map $F\to M$ and simplifies computations quite a lot.

Abstract: We'll continue to look at physical models coming from gauge theory. Starting from (parts of) the standard model as usual, followed by the NCG example of almost commutative manifolds and onto the goal of a gauge theory over a fuzzy'' manifold as in Perez-Sanchez.