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SUMMARY:Prym Representations and Twisted Cohomology of the Mapping Class G
 roup with Level Structures [Geometric Group Theory Oberseminar]
DTSTART:20260107T100000Z
DTEND:20260107T110000Z
DTSTAMP:20260317T064000Z
UID:indico-event-678@math-events.uni-bonn.de
DESCRIPTION:Speakers: Xiyan Zhong (MPI Bonn)\n\nThe Prym representations o
 f the mapping class group are an important family of representations that 
 come from abelian covers of a surface. They are defined on the level-ℓ m
 apping class group\, which is a fundamental finite-index subgroup of the m
 apping class group. One consequence of our work is that the Prym represent
 ations are infinitesimally rigid\, i.e. they can not be deformed. We prove
  this infinitesimal rigidity by calculating the twisted cohomology of the 
 level-ℓ mapping class group with coefficients in the Prym representation
 \, and more generally in the r-tensor powers of the Prym representation. O
 ur results also show that when r ≥ 2\, this twisted cohomology does not 
 satisfy cohomological stability\, i.e. it depends on the genus g. \n\nhtt
 ps://math-events.uni-bonn.de/event/678/
LOCATION:Endenicher Allee 60/0-008 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/678/
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