2022/10/24 by Knut Bjarte Haus, Haus, Knut Bjarte, Gereon Quick +1
Mathematics · #14F43 #32C35 #55N22 #57R19 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2210.13259
openalex publication_date 2022/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a geometric cycle model for a Hodge filtered extension of complex cobordism for every smooth manifold with a filtration on its de Rham complex with complex coefficients. Using a refinement of the Pontryagin-Thom construction, we construct an explicit isomorphism between our geometric model and the abstract model of Hodge filtered complex cobordism of Hopkins-Quick for every complex manifold with the Hodge filtration.