2003/12/11 by Riccardo Longoni, Longoni, Riccardo, Thomas Tradler +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #18D50 #55P48 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Sphingolipid Metabolism and Signaling #math.AT #msc:18D50 #msc:55P48
paper · pdf · doi:10.48550/arxiv.math/0312231
33 pages
arxiv created 2003/12/11 · openalex publication_date 2003/12/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We introduce the notion of homotopy inner products for any cyclic quadratic Koszul operad \mathcal O, generalizing the construction already known for the associative operad. This is done by defining a colored operad \mathcal O, which describes modules over \mathcal O with invariant inner products. We show that \mathcal O satisfies Koszulness and identify algebras over a resolution of \mathcal O in terms of derivations and module maps. An application to Poincaré duality on the chain level of a suitable topological space is given.