# Foliation

## Problem 139

Are polynomial growth foliations hyperfinite? Is $W^{ws}$ on $\Sigma ^+_{\{0,1\}}$ Borel hyperfinite?

## Problem 114

$det (I - A)$ as a group invariant for the weak foliation $W^{wu}$, seen as a subgroup lying in some $H_m (M, \mathbb S^1)$?

## Problem 112

For a hyperbolic attractor $\Lambda$ of dimension $r$, does $W^s(x) \cap \Lambda$contain a disk of dimension $k := r- Dim W^u (x)?$

## Problem 83

Unstable foliations of Anosov diffeos are given by some nilpotent group action.

## Problem 82

(Plante) A codimension one minimal foliation has at most one invariant measure

## Problem 65

Foliation ergodic theory

1. Ambrose Kakutani (in particular, question 39)
2. Does mixing make any sense? (use category, differentiability, $C^\infty$, analytic structure)
3. Averaging procedure difficulties:
• ergodic theorems, existence of invariant measures, ergodic decomposition, unique ergodicity and uniform convergence.
• polynomial growth  ...
4. Look at some specific foliations
5. Plante's stuff on connections with homology
6. Does pointwise entropy make sense?

## Problem 52

Define $\Omega$(foliation). Does $h >0$ make sense?

## Problem 51

Look for invariant measures of some standard foliations.

## Problem 9

Unique ergodicity of $W^u$ for partially Anosov diffeos.