Math 277x: Foliations and the topology of 3-manifolds. Fall 2001 |
Description of topics |
In this course we will study 2-dimensional foliations and laminations, mostly in the context of 3-manifold topology. In the last few years it has become apparent that there are deep connections between the theory of taut foliations and the Thurston theory of geometric structures on 3-manifolds. Tools from the geometric study of Riemann surfaces - train tracks, geodesic laminations, quasiconformal deformations, etc. - can be adapted to this context, and provide new avenues for the 1-dimensional complex analyst to explore.
The aim of the course is to give an exposition of some of these results which are not widely available. In particular, we will show that 3-manifolds with essential laminations satisfy the "weak geometrization conjecture", and we will discuss the extent to which the tools of taut foliation theory can be generalized to a "coarse" context.
Available for download |
References |
Required texts
Papers
Foliation links |
Foliations resources
last updated: 14th November 2001 If you have any comments on the material in this page, contact Danny Calegari via email. The applet to the right demonstrates the foliation of the plane by parabolas tangent to second order to a cubic curve. The two slides control the third degree term of the cubic, and the speed/quality of the drawing respectively. |