There are no phantom cohomology operations in K-theory
The main theorem of this paper deals with cohomology operations in connected K-theories. A stable cohomology operation between cohomology theories \(h^*_ 1\to h_ 2^*\) is called phantom if it induces the zero operation when restricted to finite complexes. An \(\Omega\)- represented operation is called completely phantom if it vanishes on all CW complexes. It is proved that there are no (non-zero) phantom or completely phantom operations between the various connected K-theories. In the course of proving this theorem the author performs a great service to homotopy theorists by going through his clear and precise versions of (inverse) limit theories for moduli spaces and spectra, the Atiyah- Hirzebruch and Dold spectral sequences and stable homotopy theory. The latter is studied in the framework of Quillen's axiomatic homotopy theory. As the author has his particular applications in mind, clarity and accuracy replace complete generality.
cohomology operations in connected K-theories
scientific article; zbMATH DE number 3877975