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UID:20250918T093422EDT-56798k1BOn@132.216.98.100
DTSTAMP:20250918T133422Z
DESCRIPTION:Title: The thorny search for a spine.\n\nAbstract: A spine for 
 a group G acting properly discontinuously on a space E is a subset onto wh
 ich there is a G-equivariant deformation retraction of E. For the space of
  lattices of covolume 1 in R^n\, the action of SL_n(Z) admits a spine of m
 inimal dimension called the well-rounded retract\, consisting of the latti
 ces whose shortest nonzero vectors span R^n. Whether an analogous spine of
  dimension 4g-5 exists for the action of the mapping class group on the Te
 ichmuller space of closed hyperbolic surfaces of genus g is an open proble
 m. In a 1985 preprint\, Thurston claimed to prove that the set X_g of surf
 aces of genus g whose systoles (the shortest closed geodesics) fill (cut t
 he surfaces into polygons) is a spine for the mapping class group. However
 \, his argument had a serious gap. Whether or not X_g is a spine\, I will 
 explain why its dimension is strictly larger than 4g-5 in certain genera. 
 The same construction shows that the set of surfaces whose systoles genera
 te a finite-index subgroup in homology (a closer analogue of the well-roun
 ded retract) does not contain any spine.\n
DTSTART:20231004T190000Z
DTEND:20231004T200000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Maxime Bourque (Université de Montréal)
URL:/mathstat/channels/event/maxime-bourque-universite
 -de-montreal-351587
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