The study of three-manifolds via their Heegaard splittings was initiated by Poul Heegaard in 1898 in his thesis. Our approach to the subject is through almost normal surfaces, as introduced by Hyam Rubinstein [Geo. Top. (Athens), 1993] and distance, as introduced by John Hempel [Topology, 2001].

Among the results presented is a proof that every closed, orientable three-manifold has only finitely many Heegaard splittings with distance greater than 4, a new recognition algorithm for surface bundles over the circle, and a series of results which bound the distance of a splitting in terms of its structure as an almost normal surface.

If you have any questions or corrections please contact me via email.

The copyright on this thesis is held by Saul Schleimer.

last touched - Jan. 2005