Poincare duality and commutative differential graded algebras

2007/01/10 by Pascal Lambrechts, Lambrechts, Pascal, Don Stanley +1 · 1 citation
Mathematics · #55M05 #55P62 #57P10 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0701309

openalex publication_date 2007/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincare duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincare duality in the same dimension. This has application in particular to the study of CDGA models of configuration spaces on a closed manifold.

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