Cohomology of unitary and symplectic groups (Q1568856)

The author carries out a standard exercise in algebraic topology. Namely he shows how one can use the Serre spectral sequence to inductively compute the (integral) cohomology rings of \(SU(n)\) and \(Sp(n)\) for all \(n\geq 2\), as well as the (integral) cohomology rings of the corresponding Stiefel varieties \(SU(n)/SU(n-k)\) and \(Sp(n)/Sp(n-k)\) for \(n\geq 1\) and \(1\leq k\leq n\). For an alternative description of the same argument we would like to refer the interested reader to \S 5.2.1~in \textit{J. McCleary}'s textbook ``User's guide to spectral sequences'' (1985; Zbl 0577.55001).