JournalscmhVol. 80 , No. 4DOI 10.4171/cmh/31

On the Γ\Gamma-cohomology of rings of numerical polynomials

  • Andrew Baker

    University of Glasgow, UK
  • Birgit Richter

    Universität Hamburg, Germany
On the $\Gamma$-cohomology of rings of numerical polynomials cover


We investigate Γ\Gamma-cohomology of some commutative cooperation algebras EEE_*E associated with certain periodic cohomology theories. For KU and E(1)E(1), the Adams summand at a prime pp, and for KO we show that Γ\Gamma-cohomology vanishes above degree 1. As these cohomology groups are the obstruction groups in the obstruction theory developed by Alan Robinson we deduce that these spectra admit unique EE_\infty structures. As a consequence we obtain an EE_\infty structure for the connective Adams summand. For the Johnson--Wilson spectrum E(n)E(n) with n1n\geq1 we establish the existence of a unique EE_\infty structure for its InI_n-adic completion.