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 cohomology of the n-torus

Posted in math.AT, tagged fixed point theorems on October 12, 2013| 13 Comments »

## The p-group fixed point theorem

Posted in math.CO, math.GR, math.NT, tagged finite fields, fixed point theorems, group actions, walks on graphs on July 9, 2013| 12 Comments »

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.