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On not the rational dualizing module for $\text{Aut}(F_n)$

By Zachary Himes

Bestvina--Feighn proved that $\text{Aut}(F_n)$ is a rational duality group, i.e. there is a $\mathbb{Q}[\text{Aut}(F_n)]$-module, called the rational dualizing module, and a form of Poincar\'e duality relating the rational cohomology of $\text{Aut}(F_n)$ to its homology with coefficients in this module. Bestvina--Feighn's proof does not give an explicit combinatorial description of the rational dualizing module of $\text{Aut}(F_n)$. But, inspired by Borel--Serre's description of the rational dualizing module of arithmetic groups, Hatcher--Vogtmann 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.

Information about the video

  • Date of recording 28/06/2022
  • Date of publication 03/12/2025
  • Institution Institut Fourier
  • Language English
  • Format MP4

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