UC Davis

Math280 (Spring 2005) - Topics in 3-manifolds

 

Organization

 

Instructor:

Prof. J Hyam Rubinstein
rubin(AT)math(dot)ucdavis(dot)edu
Office hours Tues/Thur 2-3 (655 Kerr)

Room/time:

Room 593 Kerr, Tues/Thur 11-12.30

Room 693 Kerr, Wed 2-3 for the more advanced topics, which will be optional.

 

Syllabus:

There will be two parts of the course;

1) A discussion of the basic results of classical 3-manifold theory, Heegaard splittings and connected sums,. Dehn's lemma and the loop theorem, Waldhausen's theory of Haken manifolds and JSJ theory of characteristic varieties, all from the viewpoint of normal surfaces and very short hierarchies. The aim is to get to a direct proof of word hyperbolicity of the fundamental groups of irreducible atoroidal 3-manifolds.

2) (Optional) Sweepouts and almost normal surfaces. Here we will discuss generalized sweepouts and how these can be used for minimax arguments.

Polyhedral geometry of 3-manifolds, including cubings of non-positive curvature and an introduction to higher dimensional cubical resolutions of 3-manifolds

Assessment   This will be by assignments, every two weeks.

Handouts     

These will be chapters of the CBMS lecture notes book in preparation ( due for completion July 2005)