# On the $\Gamma$-cohomology of rings of numerical polynomials

### Andrew Baker

University of Glasgow, UK### Birgit Richter

Universität Hamburg, Germany

## Abstract

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.

## Cite this article

Andrew Baker, Birgit Richter, On the $\Gamma$-cohomology of rings of numerical polynomials. Comment. Math. Helv. 80 (2005), no. 4, pp. 691–723

DOI 10.4171/CMH/31