Algebraic & Geometric Topology 12 (2012) 1405–1441

DOI: 10.2140/agt.2012.12.1405

Abstract

We construct a free and transitive action of the group of bilinear forms Bil(I ∕ I²[1]) on the set of R–products on F, a regular quotient of an even E_∞–ring spectrum R with F_*≅R_* ∕ I. We show that this action induces a free and transitive action of the group of quadratic forms QF(I ∕ I²[1]) on the set of equivalence classes of R–products on F. The characteristic bilinear form of F introduced by the authors in a previous paper is the natural obstruction to commutativity of F. We discuss the examples of the Morava K–theories K(n) and the 2–periodic Morava K–theories K_n.

Keywords

structured ring spectra, Bockstein operation, Morava K–theory, stable homotopy theory, derived category

Mathematical Subject Classification

Primary: 55P42, 55P43, 55U20

Secondary: 18E30

References

Publication

Received: 9 March 2011
Accepted: 24 February 2012
Published: 23 June 2012

Authors