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SUMMARY:Nicolás Matte Bon: "Locally moving groups acting on the real line
"
DTSTART;VALUE=DATE-TIME:20200707T080000Z
DTEND;VALUE=DATE-TIME:20200707T090000Z
DTSTAMP;VALUE=DATE-TIME:20200920T235318Z
UID:indico-event-5869@indico.math.cnrs.fr
DESCRIPTION:Abstract: A group G of homeomorphisms of the real line is loca
lly moving if every open interval supports a subgroup which acts on it wit
hout global fixed points. An example of such group is Thompson's group F.\
nIn this talk\, given a locally moving group G\, I will investigate ri
gidity and flexibility properties of the possible actions of G on the line
. It turns out that many locally moving groups (and in particular Thompson
's groups F) admit rich (uncountable) families of ``exotic'' actions whi
ch are not semi-conjugate to their ``natural'' locally moving action. Afte
r giving some examples\, I will discuss a result showing all such actions
satisfy a specific type of topological dynamical behaviour. Among applicat
ions\, we will see that if G is locally moving\, then all its actions on t
he real line by C^1-diffeomorphisms must be semi-conjugate to its locally
moving action\, and that under some additional conditions\, a locally mo
ving action is structurally stable under small deformations.\nThis is a jo
int work with Joaquín Brum\, Cristóbal Rivas and Michele Triestino.\n\nh
ttps://indico.math.cnrs.fr/event/5869/
LOCATION:
URL:https://indico.math.cnrs.fr/event/5869/
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