Algebraic & Geometric Topology

Quadratic forms classify products on quotient ring spectra

Alain Jeanneret and Samuel Wüthrich

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715403

Digital Object Identifier
doi:10.2140/agt.2012.12.1405

Mathematical Reviews number (MathSciNet)
MR2966691

Zentralblatt MATH identifier
1250.55004

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.agt/1513715403


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