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SUMMARY:On not the rational dualizing module for Aut(F_n) - Zachary Himes 
 (Cambridge)
DTSTART:20221109T160000Z
DTEND:20221109T170000Z
UID:TALK185108@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:Bestvina--Feighn proved that Aut(F_n) is a rational duality gr
 oup\, i.e. there is a Q[Aut(F_n)]-module\, called the rational dualizing m
 odule\, and a form of Poincare duality relating the rational cohomology of
  Aut(F_n) to its homology with coefficients in this module. Bestvina--Feig
 hn's proof does not give an explicit combinatorial description of the rati
 onal dualizing module of Aut(F_n). But\, inspired by Borel--Serre's descri
 ption of the rational dualizing module of arithmetic groups\, Hatcher--Vog
 tmann constructed an analogous module for Aut(F_n) and asked if it is the 
 rational dualizing module. In work with Miller\, Nariman\, and Putman\, we
  show that Hatcher--Vogtmann's module is not the rational dualizing module
 .
LOCATION:MR13
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