On not the rational dualizing module for Aut(F_n)

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• Zachary Himes (Cambridge)
• Wednesday 09 November 2022, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Oscar Randal-Williams.

Bestvina—Feighn proved that Aut(F_n) is a rational duality group, i.e. there is a Q[Aut(F_n)]-module, called the rational dualizing module, and a form of Poincare duality relating the rational cohomology of 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 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.

This talk is part of the Differential Geometry and Topology Seminar series.

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