Geometry of random Heegaard splittings

Alessandro Sisto (Heriot-Watt University)

Monday 9th May, 2022 16:00-17:00 Maths 110B + Online

Abstract

Every (closed connected oriented) 3-manifold admits a Heegaard splitting, that is to say, all 3-manifolds can be obtained gluing two handlebodies together. It is then natural to study the geometry of manifolds obtained choosing the gluing map at random, meaning using a random walk. It is known due to Maher (and geometrisation) that this construction yields hyperbolic manifolds with asymptotic probability one. However, Maher's proof doesn't give information about the hyperbolic metric besides its existence. I will outline a different construction (not relying on geometrisation) that allows one to understand a lot more about the geometry of the resulting hyperbolic metric, and can be used to study the asymptotics of volume and injectivity radius, for instance. Joint work with Peter Feller and Gabriele Viaggi.

The speaker will be in person but you may attend the talk via Zoom (link https://uofglasgow.zoom.us/j/9807879895, the passcode is the genus of the two-dimensional sphere - 4 letters all lowercase).

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