Nishida Relations in Bordism and Homology (extended abstract)

This is the second of a series of Compte Rendus. In the first [1] we have presented a theory of Dyer-Lashof operations in unoriented bordism. Here we shall discuss the (Nishida) relations between Dyer-Lashof and Landweber-Novikov operations. They are used to represent the algebra $N_{\ast }\mathrm{\Sigma }$ of covering manifolds in terms of their homology characteristic numbers. The proofs are based on the properties of the covering space operations and the notions of D-ring and Q-ring introduced in [1].