The Casson invariants of random Heegaard splittings

Joseph Maher (CUNY Staten Island)


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.

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