2001/11/30 by D. Kotschick, Thomas Vogel, T. Vogel
Computer Science · Mathematics · #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.DS #math.GT #msc:37C10 #msc:37C40 #msc:37C85 #msc:57R30
paper · pdf · doi:10.1017/s0143385702001219
published as Ergodic Theory Dynam. Systems 23 (2003), 541--558. · minor corrections, to appear in Ergodic Theory and Dynamical Systems
arxiv created 2002/04/11 · openalex publication_date 2003/03/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize the average asymptotic linking number of a pair of divergence-free vector fields on homology three-spheres by considering the linking of a divergence-free vector field on a manifold of arbitrary dimension with a codimension-two foliation endowed with an invariant transverse measure. We prove that the average asymptotic linking number is given by an integral of Hopf type. Considering appropriate vector fields and measured foliations, we obtain an ergodic interpretation of the Godbillon–Vey invariant of a family of codimension-one foliations discussed by Kotschick (Symplectic and Contact Topology: Interactions and Perspectives. Eds. Y. Eliashberg, B. Khesin and F. Lalonde. American Mathematical Society, Providence, RI).