Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 12, Number 3 (2012), 1405-1441.
Quadratic forms classify products on quotient ring spectra
We construct a free and transitive action of the group of bilinear forms on the set of –products on , a regular quotient of an even –ring spectrum with . We show that this action induces a free and transitive action of the group of quadratic forms on the set of equivalence classes of –products on . The characteristic bilinear form of introduced by the authors in a previous paper is the natural obstruction to commutativity of . We discuss the examples of the Morava –theories and the –periodic Morava –theories .
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
Permanent link to this document
Digital Object Identifier
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
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