

Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 1
By Barbara Schapira


Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 2
By Barbara Schapira
Appears in collection : Big Mapping Class Groups and Diffeomorphism Groups / Gros groupes modulaires et groupes de difféomorphismes
The study of the path-connectedness of the space of $C^{r}$ actions of $\mathbb{Z}^{2}$ on the interval [0,1] plays an important role in the classification of codimension 1 foliations on 3 manifolds. One way to deform actions is by conjugation. If an action can be brought arbitrarily close to the trivial one by conjugation, it is said to be quasi-reducible. In this talk, we will present and compare obstructions to quasi-reducibility in different regularity classes, and draw conclusions concerning the initial connectedness problem.