*Ma 157b* - Introduction to 3-manifolds; Spring 2003

### Instructor: Danny Calegari

### MWF 12-1 153 Sloan

### Grading policy:

One homework problem will be given out each Friday. This homework
is due at the start of class the following Friday.

### Description of course:

An introduction to the topology of 3-manifolds.
This class will concentrate on the multiplicity of important and natural
structures on 3-manifolds, and the ways in which these
different points of view interact to reveal deep topological insights.
One prominent theme will be the interaction of topology with certain
kinds of geometric structures, which give the subject at times an
algebraic or combinatorial flavour, at times a metric or differential
flavour, and at times a dynamical flavour.

### Topics to be covered (if time allows):

- Basic descriptions of 3-manifolds: triangulations, Heegaard diagrams,
Kirby calculus
- Homotopy and isotopy: Dehn's lemma, the loop theorem and the sphere theorem
- Incompressible tori: Seifert fibered spaces, torus bundles, JSJ decomposition
- Incompressible surfaces: Haken manifolds, hierarchies, algorithmic theory of 3-manifolds
- Geometric structures, and the geometrization conjecture
- Dynamics on 3-manifolds: flows, foliations and contact structures

### References:

- A. Hatcher
*Basic topology of 3-manifolds* available from Hatcher's web page
- J. Hempel
*Three manifolds* Princeton University Annals of Mathematics Study 86 (1976)
- W. Jaco
*Lectures on three-manifold topology* CBMS series volume 43 (1980)
- D. Rolfsen
*Knots and links* Publish or Perish volume 7 (1976)
- W. Thurston
*Three dimensional Geometry and Topology* Princeton Mathematical Series vol. 35 (1997)