2020/04/15 by Pavel Hajek, Hajek, Pavel
Mathematics · #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2004.07362
openalex publication_date 2020/04/15 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/30
We extend a CDGA V with a perfect pairing of degree n on cohomology to a CDGA V with a pairing of degree n on chain level such that V admits a Hodge decomposition and retracts onto V preserving the pairing on cohomology; here we suppose that V is either 1-connected, or that V is connected, of finite type, and n is odd. We show that a Hodge decomposition of V induces a differential Poincaré duality model of V in a natural way. Assuming that H(V) is 1-connected, we apply our extension to a Sullivan model of V in the proof of the existence and "uniqueness" of a 1-connected differential Poincaré duality model of V by Lambrechts & Stanley; we eliminate their extra assumptions in the uniqueness statement, including H2(V)=0 if n is odd.