Math 277x: Foliations and the topology of 3-manifolds. Fall 2001

Instructor: Danny Calegari

MWF 12-1 SC 113

Rationale: to give an exposition of some recent developments in the theory of foliations and laminations of 3-manifolds, and their relation to the geometrization conjecture.

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.

Prerequisites: Some background in the Thurston theory of 3-manifolds. Familiarity with basic algebraic and geometric topology, and complex analysis of one variable.

Available for download

Note: this material is incomplete and should not be circulated or mirrored without first asking permission. The problem list is preliminary, and I actively invite corrections, comments or suggestions at this stage.


Required texts



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.

Danny Calegari's home page

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