De Rham Cohomology of SO(n) by Supersymmetric Quantum Mechanics
  We give an elementary derivation of the de Rham cohomology of SO(n) in terms of supersymmetric quantum mechanics. Our analysis is based on Witten's Morse theory. We show reflection symmetries of the theory are useful to select true vacuums. The number of the selected vacuums will agree with the de Rham cohomology of SO(n). 
Kazuto Oshima