Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Hyperbolic volume of links, via pants graphs and train tracks

Antonio De Capua

created by daniele on 07 Apr 2015

8 apr 2015 -- 16:00

Sala Seminari, DM, Pisa

Seminari di Geometria, Pisa


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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