The goal of this post is to compute the cohomology of the -torus in as many ways as I can think of. Below, if no coefficient ring is specified then the coefficient ring is by default. At the end we will interpret this computation in terms of cohomology operations.
Posts Tagged ‘fixed point theorems’
The goal of this post is to collect a list of applications of the following theorem, which is perhaps the simplest example of a fixed point theorem.
Theorem: Let be a finite -group acting on a finite set . Let denote the subset of consisting of those elements fixed by . Then ; in particular, if then has a fixed point.
Although this theorem is an elementary exercise, it has a surprising number of fundamental corollaries.