Lecture 1 (Monday): Casson's approach to triangulations and the connection to normal surface theory.
Lecture 2 (Monday): Branch points and the theory of normal surfaces.
Lecture 3 (Tuesday): Immersed incompressible surfaces in hyperbolic triangulations.
Lecture 4 (Tuesday): Cubings.
Lecture 5 (Wednesday): Strongly irreducible splittings.
Lecture 6 (Wednesday): Comparing heegaard splittings.
Lecture 7 (Thursday): Almost normal surfaces.
Lecture 8 (Thursday): Finiteness of heegaard splittings.
Lecture 9 (Friday): Group actions on the 3-sphere.
Lecture 10 (Friday): Higher order sweepouts and thin position.

Lecture 1: (Monday) Fundamental Notions and Applications to Haken Manifolds.
A very quick review of basic notions; sketch how one gets least weight essential spheres, disks, tori, and incompressible surfaces being fundamental (hint at how one gets these at verticies); applications to Haken manifolds such as finiteness of incompressible surfaces of a fixed genus up to Dehn twists and isotopy; construction of hierarchies; and how the homeomorphism problem is done.

Lecture 2: (Tuesday) Geography of the Projective Solution Space and Algorithms.
Irreducible and characteristic decompositions being at vertices; faces of incompressible surfaces, faces of taut surfaces; faces carrying homology and relationship of the projective solution space and Thurston's norm, non-rational points and foliations, algorithms based on pseudo-triangulations with only one vertex and applications to knot theory.

Lecture 1: (Thursday) Thin position and almost normal surfaces.
Lecture 2: (Friday) Recognizing the 3-sphere.

Other Events:

(1) There will be a party on Monday night. Check back for details.
(2) There will be a barbeque at the Recreation Pool on Wednesday evening.

5-28-96

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