2010/01/12 by Dev Sinha, Sinha, Dev · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #57T30 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Sphingolipid Metabolism and Signaling #math.AT #msc:57T30
paper · pdf · doi:10.48550/arxiv.1001.2032
From a presentation given at the Luminy conference on operads in 2009. 9 pages, two figures
arxiv created 2010/01/12 · openalex publication_date 2010/01/12 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We survey the topology which led to the original bar and cobar constructions, for both associative algebras and coalgebras and for Lie algebras and commutative coalgebras. These constructions are often viewed as part of the larger theory of Koszul duality of operads, so this survey is meant to offer an historical perspective on the most prominent cases of that theory. We also explain recent work which shows that Hopf/linking invariants for homotopy are at the heart of the duality between commutative algebras and Lie coalgebras.