- #1

electroweak

- 44

- 1

For a compact Lie group we have the very useful property, due to Borel, that with real coefficients all odd cohomology vanishes: H^odd(BG; R) = 0. So the odd cohomology (and homology) consists completely of torsion. For finite groups an even stronger result holds: all cohomology is finite: H(BG; R) = 0.

Why are either of these statements (the Lie group case or the finite case) true?