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

摘要

We examine the Weyl invariant subringH*(BT)Wof the integral singular cohomology ringH*(BT) of the classifying spaceBTof the maximal torusTin a connected compact Lie groupK. We show thatH*(BT)Wis not a polynomial algebra forK= Spin(n) whenn#x2265;10. We describe the connection of this result with the Borel homomorphismH*{BT) #x2192;H*{K/T).