Cohomology of measurable laminations

On the vanishing of the measurable Schur cohomology groups of Weil groups

We generalize a theorem of Tate and show that the second cohomology of the Weil group of a global or local field with coefficients in C∗ (or, more generally, with coefficients in the complex points of an algebraic torus over C) vanish, where the cohomology groups are defined using measurable cochains in the sense of Moore. We recover a theorem of Labesse stating that the admissible homomorphism...

R-trees and laminations for free groups I: Algebraic laminations

This paper is the first of a sequence of three papers, where the concept of an Rtree dual to (the lift to the universal covering of) a measured geodesic lamination L in a hyperbolic surface S is generalized to arbitrary R-trees provided with a (very small) action of the free group FN of finite rank N ≥ 2 by isometries. In [CHL-II] to any such R-tree T a dual algebraic lamination L(T ) is associ...

Non-euclidean Affine Laminations

The purpose of the present paper is to discuss examples of aane Riemann surface laminations which do not admit a leafwise Euclidean structure. The rst example of such a lamination was constructed by Ghys Gh97]. Our discussion is based on the geometric methods developed by Lyubich, Minsky and the author LM97], KL01], which rely on the observation that any aane surface A gives rise in a natural w...

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

Laminations in Holomorphic Dynamics