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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Counting loxodromics for hyperbolic actions - Samu
el Taylor (Yale University)
DTSTART;TZID=Europe/London:20170109T143000
DTEND;TZID=Europe/London:20170109T153000
UID:TALK69869AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/69869
DESCRIPTION:Consider a nonelementary action by isometries of a
hyperbolic group G on a hyperbolic metric space X
. Besides the action of G on its Cayley graph\, so
me examples to bear in mind are actions of G on tr
ees and quasi-trees\, actions on nonelementary hyp
erbolic quotients of G\, or examples arising from
naturally associated spaces\, like subgroups of th
e mapping class group acting on the curve graph. <
br> We show that the set of elements of G which ac
t as loxodromic isometries of X (i.e those with si
nk-source dynamics) is generic. That is\, for any
finite generating set of G\, the proportion of X-l
oxodromics in the ball of radius n about the ident
ity in G approaches 1 as n goes to infinity. We al
so establish several results about the behavior in
X of the images of typical geodesic rays in G. Fo
r example\, we prove that they make linear progres
s in X and converge to the boundary of X. This is
joint work with I. Gekhtman and G. Tiozzo.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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