On classification of Heegaard splittings (Q1371128)

A closed 3-manifold of course admits many Heegaard splittings. Even if the genus is fixed and two splittings are considered equivalent if the splitting surfaces are isotopic there may still be many inequivalent splittings. This paper studies Heegaard splittings of a certain technically defined class of 3-manifolds. This class includes cusped hyperbolic manifolds with (1) geodesic boundary. The author is able to characterize the splittings under certain hypotheses too technical to describe here.