Polynomial operations on stable cohomotopy
Following ideas of G. Segal, the author gives a conceptual framework for the study of a wide class of unstable operations from the 0th stable cohomotopy group \(\pi^ 0_ s\) to other homotopy functors. These include symmetric powers especially. The concept of polynomial operations is defined and one gets a ring \(Pol(\pi^ 0_ s,\pi^ 0_ s)\). This ring is isomorphic to \(Pol(A,\hat A)\) where A is the Burnside ring and \(\hat A\) is the completed Burnside functor using augmentation ideals. Here the Pol denotes the ring of polynonial maps. This isomorphism is the paper's main result. The paper mentions characteristic classes, K-theory, and transfers of finite coverings.
scientific article; zbMATH DE number 4163739
scientific article