Geodesic
Quadratic forms classify products on quotient ring spectra
Jeanneret, Alain1 ; Wüthrich, Samuel2
1Mathematisches Institut, Sidlerstrasse 5, CH-3012 Berne, Switzerland
2SBB, Brückfeldstrasse 16, CH-3000 Bern, Switzerland
Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1405-1441
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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 Kn.

DOI : 10.2140/agt.2012.12.1405
Classification : 55P42, 55P43, 55U20, 18E30
Keywords: structured ring spectra, Bockstein operation, Morava $K$–theory, stable homotopy theory, derived category

Jeanneret, Alain  1   ; Wüthrich, Samuel  2

1 Mathematisches Institut, Sidlerstrasse 5, CH-3012 Berne, Switzerland
2 SBB, Brückfeldstrasse 16, CH-3000 Bern, Switzerland 
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Jeanneret, Alain; Wüthrich, Samuel. Quadratic forms classify products on quotient ring spectra. Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1405-1441. doi: 10.2140/agt.2012.12.1405

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