Resumen de On the $\Gamma$-cohomology of rings of numerical polynomials

Andrew Baker, Birgit Richter

• We investigate $\Gamma$-cohomology of some commutative cooperation algebras $E_*E$ associated with certain periodic cohomology theories. For KU and $E(1)$, the Adams summand at a prime $p$, and for KO we show that $\Gamma$-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 $E_\infty$ structures. As a consequence we obtain an $E_\infty$ structure for the connective Adams summand. For the Johnson--Wilson spectrum $E(n)$ with $n\geq1$ we establish the existence of a unique $E_\infty$ structure for its $I_n$-adic completion.