English

Linking numbers of measured foliations

Geometric Topology 2007-05-23 v3 Dynamical Systems

Abstract

We generalise 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 in math.GT/0111137.

Keywords

Cite

@article{arxiv.math/0111209,
  title  = {Linking numbers of measured foliations},
  author = {D. Kotschick and T. Vogel},
  journal= {arXiv preprint arXiv:math/0111209},
  year   = {2007}
}

Comments

minor corrections, to appear in Ergodic Theory and Dynamical Systems

R2 v1 2026-07-22T16:41:40.231Z