We outline several ways to define cohomology groups naturally associated to Lie groups. Each of them has a different motivation, along with its merits and drawbacks. We then discuss a method for proving that (almost) all of the definitions are in fact isomorphic. A particular emphases will be on the string class of a compact and simple Lie group.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/3946