GALOIS COHOMOLOGY AND COMPONENT GROUP OF A REAL REDUCTIVE GROUP

Let G be a connected reductive group over the field of real numbers R. Using results of our previous joint paper, we compute combinatorially the first Galois cohomology set H-1 (R, G) in terms of reductive Kac labelings. Moreover, we compute the group of connected components pi(0)G(R) of the real Lie group G(Double-struck capital R) and the maps in exact sequences containing pi(0)G(R) and H-1(R, G).