The Casson invariant for random Heegaard splittings

Joseph Maher (CUNY)

The mapping class group element resulting from a finite length random walk on the mapping class group may be used as the gluing map for a Heegaard splitting, and the resulting 3-manifold is known as a random Heegaard splitting. We use these to show the existence of infinitely many closed hyperbolic 3-manifolds with any given value of the Casson invariant. This is joint work with Alex Lubotzky and Conan Wu.