Algebraic & Geometric Topology

Quadratic forms classify products on quotient ring spectra

Alain Jeanneret and Samuel Wüthrich

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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.

Article information

Algebr. Geom. Topol., Volume 12, Number 3 (2012), 1405-1441.

Received: 9 March 2011
Accepted: 24 February 2012
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P42: Stable homotopy theory, spectra 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 55U20: Universal coefficient theorems, Bockstein operator
Secondary: 18E30: Derived categories, triangulated categories

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


Jeanneret, Alain; Wüthrich, Samuel. Quadratic forms classify products on quotient ring spectra. Algebr. Geom. Topol. 12 (2012), no. 3, 1405--1441. doi:10.2140/agt.2012.12.1405.

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