Homology and cohomology of E? ring spectra

2004/07/12 by Maria Basterra, Michael A. Mandell · 3 citations
Chemistry · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Amino acid #Chemistry #Cohomology #Cohomology ring #De Rham cohomology #Equivariant cohomology #Group cohomology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Mayer–Vietoris sequence #Pure mathematics #math.AT #math.QA #msc:55P43 #msc:55P48 #msc:55U35

paper · pdf · doi:10.1007/s00209-004-0744-y

published as Math. Z. 249 (2005), no. 4, 903-944

arxiv created 2004/07/12 · openalex publication_date 2005/01/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Every homology or cohomology theory on a category of E-infinity ring spectra is Topological Andre-Quillen homology or cohomology with appropriate coefficients. Analogous results hold for the category of A-infinity ring spectra and for categories of algebras over many other operads.

Citations

• André–Quillen cohomology of commutative S-algebras

Cited by

• Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory
• Homotopy theory of modules over operads in symmetric spectra
• Bar constructions and Quillen homology of modules over operads