# 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

**Abstract.**

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.