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Coarse Teichmüller geometry and train tracks

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Speaker: 
Antonio de Capua
Affiliation: 
MPIM
Date: 
Mon, 2018-07-09 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

This presentation is meant as an extended version of the summary of my
work I gave for a New Guests' Oberseminar some months ago. The first
part will be a condensed account of Teichmüller spaces, mapping class
groups of surfaces, and how one uses coarse models (the curve graph, the
marking graph, the pants graph) to get a better understanding of them.
Then I will introduce train tracks - 'drawings' on the given surface
which look like railway networks - and the dynamics generated by their
splitting sequences: I will focus on how they fit in the
coarse-geometrical study of Teichmüller theory as they give tangible
examples of quasi-geodesic sequences. This will be an occasion to state
the main result of my PhD thesis - quasi-geodicity of splitting
sequences in the pants graph - and to say a few words about its proof.
Finally, if time allows, I will mention some connections of these topics
with the geometry of 3-manifolds and/or interesting questions I am
considering for my current and future work.

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