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Quadratic forms classify products on quotient ring spectra

Alain Jeanneret and Samuel Wüthrich

Algebraic & Geometric Topology 12 (2012) 1405–1441

We construct a free and transitive action of the group of bilinear forms Bil(II2[1]) on the set of R–products on F, a regular quotient of an even E–ring spectrum R with FRI. We show that this action induces a free and transitive action of the group of quadratic forms QF(II2[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 Kn.

structured ring spectra, Bockstein operation, Morava $K$–theory, stable homotopy theory, derived category
Mathematical Subject Classification 2010
Primary: 55P42, 55P43, 55U20
Secondary: 18E30
Received: 9 March 2011
Accepted: 24 February 2012
Published: 23 June 2012
Alain Jeanneret
Mathematisches Institut
Sidlerstrasse 5
CH-3012 Berne
Samuel Wüthrich
Brückfeldstrasse 16
CH-3000 Bern