Integral weyl invariants and the borel homomorphism for spin(n)

Abstract

We examine the Weyl invariant subring H *(BT)W of the integral singular cohomology ring H *(BT) of the classifying space BT of the maximal torus T in a connected compact Lie group K. We show that H *(BT)W is not a polynomial algebra for K = Spin(n) when n ≥10. We describe the connection of this result with the Borel homomorphism H *{BT) → H *{K/T).