Cohomology of manifolds with structure group U(n)× O(s)

2022/07/08 by Paweł Raźny, Raźny, Paweł
Mathematics · #53C12 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2207.04112

openalex publication_date 2022/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new spectral sequence for the study of K-manifolds which arises by restricting the spectral sequence of a Riemannian foliation to forms invariant under the flows of \ξ₁,...,ξ_s\. We use this sequence to generalize a number of theorems from K-contact geometry to K-manifolds. Most importantly we compute the cohomology ring and harmonic forms of S-manifolds in terms of primitive basic cohomology and primitive basic harmonic forms (respectively). As an immediate consequence of this we get that the basic cohomology of S-manifolds are a topological invariant. We also show that the basic Hodge numbers of S-manifolds are invariant under deformations. Finally, we provide similar results for C-manifolds.

Related

• Frölicher spectral sequence and Hodge structures on the cohomology of complex parallelisable manifolds
• Poisson harmonic forms, Kostant harmonic forms, and the S¹-equivariant cohomology of K/T
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