$\Gamma$-cohomology of rings of numerical polynomials and $E_\infty$ structures on K-theory
Algebraic Topology
2007-05-23 v3
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 infinity structures. As a consequence we obtain an E infinity structure for the connective Adams summand. For the Johnson-Wilson spectrum E(n) with n > 0 we establish the existence of a unique E infinity structure for its I_n-adic completion.
Keywords
Cite
@article{arxiv.math/0304473,
title = {$\Gamma$-cohomology of rings of numerical polynomials and $E_\infty$ structures on K-theory},
author = {Andrew Baker and Birgit Richter},
journal= {arXiv preprint arXiv:math/0304473},
year = {2007}
}
Comments
Revised version, to appear in Commentarii Math. Helv