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

• Autores: Andrew Baker, Birgit Richter
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 80, Nº 4, 2005, págs. 691-723
• Idioma: inglés
• DOI: 10.4171/cmh/31
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• Resumen

  • 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.