Dynamics and the Godbillon-Vey class: a history and survey
by Steven Hurder

HISTORY:

This paper grew out of a compilation of observations in preparation for the conference "Foliations: Geometry and Dynamics" at the Banach Center, Warsaw. After the conference, several papers were written on the subject of the title of this survey, and at the end of August, 2000 it was decided to write some of these observations into a formal survey.

This work updates and expands on parts of the 1989 Seminaire Bourbaki "Sur l'invariant de Godbillon-Vey" by Etienne Ghys, which it is hard to improve on. There have been several developments since that time, however, which deserve a discussion, including the various works on minimal sets, ideas from the problem session from the 1992 foliations meeting in Rio de Janeiro, and more recent ideas and work of the author.

The bibliography takes advantage of the recent posting by Philippe Tondeur of the bibliography to his book, which makes it much easier to search for papers on the subject during the period 1940 to 1995. So part of the project included compiling a comprehensive and up-to-date bibliography.