Lectures on Foliation Dynamics: Barcelona 2010

TL;DR

This survey introduces key concepts and recent developments in foliation dynamical systems, emphasizing classification and active research topics, with informal discussion, references, open questions, and exercises for further exploration.

Contribution

It provides an updated, comprehensive overview of foliation dynamics, integrating recent progress and highlighting open problems in the classification of foliations on compact manifolds.

Findings

Summarizes recent advances in foliation dynamical systems

Highlights open problems and research directions

Includes exercises for further study

Abstract

This survey is based on a series of five lectures, given May 3--7, 2010, at the Centre de Recerca Matematica, Barcelona. The goal of the lectures was to present aspects of the theory of foliation dynamical systems which have particular importance for the classification of foliations of compact manifolds. The lectures emphasized intuitive concepts and informal discussion, while taking the reader into topics of active research in this subject. These notes update and expand on the lectures, and include more recent progress. This article also includes an extensive set of references, as well as highlighting many open questions and problems. A set of "homework problems" is also included, one for each day of lecture.