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Big mapping class groups - lecture 4
Multi angle
Authors : Calegari, Danny (Author of the conference)
CIRM (Publisher )
37FXX - complex dynamical systems
57Mxx - Low-dimensional topology
Additional resources :
http://math.uchicago.edu/~dannyc/books/big_mcg/big_mcg.html
CIRM (Publisher )
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Abstract :
Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. We 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). Using these relations, we will explain how to construct non trivial quasimorphisms on subgroups of big mapping class groups. This includes joint work with Alden Walker.
Part II - Examples : In this part we will discuss a number of natural examples in which big mapping class groups and their subgroups arise. These include the inverse limit constructions of de Carvalho-Hall, the theory of finite depth (taut) foliations of 3-manifolds, the theory of “Artinization” of Thompson-like groups, two dimensional smooth dynamics, one dimensional complex dynamics (topology of the shift locus, Schottky spaces) and several other contexts. We will try to indicate how viewing these examples from the perspective of (big) mapping class groups is a worthwhile approach.
Keywords : mapping class groups; hyperbolic geometry; complex dynamics
MSC Codes : Part II - Examples : In this part we will discuss a number of natural examples in which big mapping class groups and their subgroups arise. These include the inverse limit constructions of de Carvalho-Hall, the theory of finite depth (taut) foliations of 3-manifolds, the theory of “Artinization” of Thompson-like groups, two dimensional smooth dynamics, one dimensional complex dynamics (topology of the shift locus, Schottky spaces) and several other contexts. We will try to indicate how viewing these examples from the perspective of (big) mapping class groups is a worthwhile approach.
Keywords : mapping class groups; hyperbolic geometry; complex dynamics
37FXX - complex dynamical systems
57Mxx - Low-dimensional topology
Additional resources :
http://math.uchicago.edu/~dannyc/books/big_mcg/big_mcg.html
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 11/06/2019 Conference Date : 23/05/2019 Subseries : Research School arXiv category : Dynamical Systems ; Geometric Topology Mathematical Area(s) : Dynamical Systems & ODE ; Topology Format : MP4 (.mp4) - HD Video Time : 00:54:52 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-05-23_Calegari_Part4.mp4 
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Information on the Event
Event Title : Dynamique au-delà de l'hyperbolicité uniforme / Dynamics Beyond Uniform HyperbolicityEvent Organizers : Bonatti, Christian ; Buzzi, Jérôme ; Crovisier, Sylvain ; Gan, Shaobo ; Pacifico, Maria José Dates : 13/05/2019 - 24/05/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/1947.html
Citation Data
DOI : 10.24350/CIRM.V.19526103Cite this video as: Calegari, Danny (2019). Big mapping class groups - lecture 4. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19526103 URI : http://dx.doi.org/10.24350/CIRM.V.19526103 |
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