2010/04/06 by Alain Jeanneret, Jeanneret, Alain, Samuel Wuethrich +1
Chemistry · Mathematics · #18E30 (Secondary) #55P42 #55P43 (Primary) #55U20 #Advanced Topics in Algebra #Algebra over a field #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Bilinear form #Chemistry #Clifford algebra #Cohomology #Cohomology ring #Equivariant cohomology #FOS: Mathematics #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Physics #Pure mathematics #Quotient #Quotient ring #Ring (chemistry) #Spectrum (functional analysis) #math.AT #msc:18E30 #msc:55P42 #msc:55P43 #msc:55U20
paper · pdf · doi:10.48550/arxiv.1004.0954
Final version (to appear). Changes: new paragraph in 1.1, amended Definition 2.14, new Remark 3.6, amended proof of Proposition 5.1 (reference problem eliminated), various minor changes
openalex publication_date 2010/04/06 · arxiv created 2011/01/21 · arxiv updated 2011/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.