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Clifford algebras from quotient ring spectra

Jeanneret, A. ; Wüthrich, S.

In: Manuscripta Mathematica, 2011, vol. 136, no. 1-2, p. 33-63

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    Title
    • Clifford algebras from quotient ring spectra
    Author
    • Jeanneret, A.. Mathematisches Institut, Sidlerstrasse 5, 3012, Bern, Switzerland
    • Wüthrich, S.. SBB, Brückfeldstrasse 16, 3000, Bern, Switzerland
    Document Type
    • Postprint
    Classification
    • Mathematics
    OAI-PMH Identifier
    • oai:doc.rero.ch:320941
    Summary
    We give natural descriptions of the homology and cohomology algebras of regular quotient ring spectra of even E ∞-ring spectra. We show that the homology is a Clifford algebra with respect to a certain bilinear form naturally associated to the quotient ring spectrum F. To identify the cohomology algebra, we first determine the derivations of F and then prove that the cohomology is isomorphic to the exterior algebra on the module of derivations. We treat the example of the Morava K-theories in detail