Hyperbolic volume of links, via pants graph and train tracks – Antonio De Capua (University of Oxford)


Sala Seminari (Dip. Matematica).


A result of Jeffrey Brock states that, given a hyperbolic 3-manifold which is a mapping torus over a surface $S$, its volume can be expressed in terms of the distance induced by the monodromy map in the pants graph of $S$. This is an abstract graph whose vertices are pants decompositions of $S$, and edges correspond to some sort of ‘elementary alterations’ of those. Brock’s theorem motivates investigation about distances in the pants graph; in particular we generalise a result of Masur, Mosher and Schleimer that train track splitting sequences (which will be defined during the talk) induce quasi-geodesics in the marking graph. This will be the core piece of a volume estimate for complements of closed braids in the solid torus.

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