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Instructor: |
Prof. J Hyam Rubinstein |
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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. |
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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.
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Handouts
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These will be
chapters of the CBMS lecture notes book in preparation ( due for completion
July 2005) |