The complex cobordism of \(BSO_n\) (Q983872)

This paper computes \(MU^{*}(BSO(2m))\). The authors show that it is generated as an \(MU^{*}\)-algebra by Conner-Floyd Chern classes \(c_{i}\) and one \(2m\)-dimensional element \(y_{m}\). Using a result of Totaro that for algebraic groups \(G\) the classifying spaces are approximated by algebraic varieties one can compute the Chow ring of \(BG\). The arguments use the stratification method introduced by Verosi, but without the algebraic geometry results. Results are also obtained for the Morava \(K\)-theory of \(BSO _{2m+1}\)