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SUMMARY:Kenneth Bromberg: "Disintegrating the curve graph"
DTSTART:20250513T120000Z
DTEND:20250513T130000Z
DTSTAMP:20260505T014600Z
UID:indico-event-14239@indico.math.cnrs.fr
DESCRIPTION:On a surface\, the curve graph\, defined by Harvey\, is a 1-c
 omplex whose vertices are isotopy class of simple closed curves and edges 
 correspond to disjointness. Masur and Minsky famously proved that this gra
 ph is Gromov hyperbolic. Here we will examine a family of similar graphs\,
  defined by Hamenstädt\, where edges are determined by a complexity condi
 tion on the two curves. More precisely rather than just asking if the two 
 curves intersect we want to measure the complexity of the intersection. Wh
 en the two curves ``fill’’ the surface (every curve intersects one of 
 the two) then complementary regions will be a collection of even sided pol
 ygons. The complexity is highest when these complementary polygons are all
  hexagons and quadrilaterals and in the principal curve graph there is a
 n edge between two curves whenever the two curves intersection is not of t
 his maximal complexity. By changing the complexity threshold we get a sequ
 ence of graphs (and maps) that interpolate between the original curve grap
 h and the principal graph. We show that principal curve graph is a quasi-t
 ree (a strong hyperbolicity condition) and\, more generally\, for any of t
 he graphs in the sequence the pre-image of a bounded set in one graph is a
  quasi-tree in the graph one level up. This is joint work with Mladen Best
 vina and Alex Rasmussen.\n\nhttps://indico.math.cnrs.fr/event/14239/
LOCATION:435 (UMPA)
URL:https://indico.math.cnrs.fr/event/14239/
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