On the Gamma-cohomology of rings of numerical polynomials and E-infinity structures on K-theory

Baker, A. and Richter, B. (2005) On the Gamma-cohomology of rings of numerical polynomials and E-infinity structures on K-theory. Commentarii Mathematici Helvetici, 80(4), pp. 691-723. (doi: 10.4171/CMH/31)

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∞ structures. As a consequence we obtain an E∞ structure for the connective Adams summand. For the Johnson-Wilson spectrum E(n) with n≥1 we establish the existence of a unique E∞ structure for its In-adic completion.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Baker, Dr Andrew
• Authors: Baker, A., and Richter, B.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Commentarii Mathematici Helvetici