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SUMMARY:A Structure Theorem for Geodesic Currents and Applications to Comp
actifications of Character Varieties
DTSTART;VALUE=DATE-TIME:20180212T133000Z
DTEND;VALUE=DATE-TIME:20180212T144500Z
DTSTAMP;VALUE=DATE-TIME:20210413T102945Z
UID:indico-event-3211@indico.math.cnrs.fr
DESCRIPTION:We find a canonical decomposition of a geodesic current on a s
urface of finite type arising from a topological decomposition of the surf
ace along special geodesics. We show that each component either is associa
ted to a measured lamination or has positive systole. For a current with p
ositive systole\, we show that the intersection function on the set of clo
sed curves is bilipschitz equivalent to the length function with respect t
o a hyperbolic metric. We show that the subset of currents with positive s
ystole is open and that the mapping class group acts properly discontinuou
sly on it. As an application\, we obtain in the case of compact surfaces a
structure theorem on the length functions appearing in the length spectru
m compactification both of the Hitchin and of the maximal character variet
ies and determine therein an open set of discontinuity for the action of t
he mapping class group. This is joint work with Alessandra Iozzi\, Anne Pa
rreau\, and Beatrice Pozzetti.\n\nhttps://indico.math.cnrs.fr/event/3211/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/3211/
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