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SUMMARY:Two simultaneous actions of big mapping class groups
DTSTART;VALUE=DATE-TIME:20190130T133000Z
DTEND;VALUE=DATE-TIME:20190130T144500Z
DTSTAMP;VALUE=DATE-TIME:20190724T043320Z
UID:indico-event-4296@indico.math.cnrs.fr
DESCRIPTION:\n \n Mapping class groups of infinite type surfaces\, also ca
lled "big" mapping class groups\, arise naturally in several dynamical con
texts\, such as two-dimensional dynamics\, one-dimensional complex dynamic
s\, "Artinization" of Thompson groups\, etc.\n\n In this talk\, I will pre
sent 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 Gromov-hyperbolic graph.
The second is an action by homeomorphisms on a circle in which the vertic
es of the graph naturally embed. I will describe some properties of the ob
jects involved\, and give some fruitful relations between the dynamics of
the two actions. For example\, we will see that loxodromic elements (for t
he first action) necessarily have rational rotation number (for the second
action). If time allows\, I will explain how to use these simultaneous ac
tions to construct nontrivial quasimorphisms on subgroups of big mapping c
lass groups.\n This is joint work with Alden Walker.\n\n\nhttps://indico.m
ath.cnrs.fr/event/4296/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/4296/
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