Clifford algebras from quotient ring spectra

Details Clifford algebras from quotient ring spectra Clifford algebras from quotient ring spectra

2010-04-06

arxiv.org/abs/1004.0954v2

Mathematics

Algebraic Topology

Final version (to appear). Changes: new paragraph in 1.1, amended Definition 2.14, new Remark 3.6, amended proof of Propositio

Scientific paper

We give natural descriptions of the homology and cohomology algebras of regular quotient ring spectra of even E-infinity 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.

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