Linking numbers of measured foliations

Details Linking numbers of measured foliations Linking numbers of measured foliations

2001-11-19

arxiv.org/abs/math/0111209v3

Ergodic Theory Dynam. Systems 23 (2003), 541--558.

Mathematics

Geometric Topology

minor corrections, to appear in Ergodic Theory and Dynamical Systems

Scientific paper

10.1017/S0143385702001219

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.

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