Status  Confirmed 
Seminar Series  MATHIHES 
Subjects  math 
Date  Wednesday 30 January 2019 
Time  14:30 
Institute  IHES 
Seminar Room  Amphithéâtre Léon Motchane 
Speaker's Last Name  Bavard 
Speaker's First Name  Juliette 
Speaker's Email Address  
Speaker's Institution  CNRS & Université de Rennes 1 
Title  Two simultaneous actions of big mapping class groups 
Abstract  Mapping class groups of infinite type surfaces, also called "big" mapping class groups, arise naturally in several dynamical contexts, such as twodimensional dynamics, onedimensional complex dynamics, "Artinization" of Thompson groups, etc. In this talk, I will present recent objects and phenomena related to big mapping class groups. In particular, I will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromovhyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. I will describe some properties of the objects involved, and give some fruitful relations between the dynamics of the two actions. For example, we will see that loxodromic elements (for the first action) necessarily have rational rotation number (for the second action). If time allows, I will explain how to use these simultaneous actions to construct nontrivial quasimorphisms on subgroups of big mapping class groups. This is joint work with Alden Walker. 
arXiv Preprint Number  
Comments  Séminaire Géométrie et groupes discrets 
Attachments 
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