Unstable splittings in Hodge filtered Brown–Peterson cohomology

2016/10/31 by Gereon Quick · 1 citation
Mathematics · #Algebra over a field #Algebraic topology #Cohomology #De Rham cohomology #Geometric and Algebraic Topology #Geometry and complex manifolds #Hodge conjecture #Hodge dual #Hodge theory #Homotopy and Cohomology in Algebraic Topology #Loop (graph theory) #Number theory #math.AG #math.AT #math.DG

paper · pdf · doi:10.1007/s40062-018-0215-5

published in Journal of Homotopy and Related Structures 14(2), 349-369 (Springer Science+Business Media) · 16 pages

openalex created_date 2016/11/04 · arxiv created 2016/11/17 · openalex publication_date 2018/09/27 · arxiv updated 2020/11/10 · openalex updated_date 2026/08/05

Abstract

We construct Hodge filtered function spaces associated to infinite loop spaces. For Brown-Peterson cohomology, we show that the corresponding Hodge filtered spaces satisfy an analog of Wilson's unstable splitting. As a consequence, we obtain an analog of Quillen's theorem for Hodge filtered Brown-Peterson cohomology for complex manifolds.

Citations

• Torsion algebraic cycles and complex cobordism
• A spectrum whose Zp cohomology is the algebra of reduced pth powers
• On the formal group laws of unoriented and complex cobordism theory
• Théorie de Hodge : II