Computing high-dimensional group cohomology via duality

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• Benjamin Brueck (ETH Zurich)
• Friday 20 January 2023, 13:45-14:45
• MR13.

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In recent years, duality approaches have yielded new results about the high-dimensional cohomology of several groups and moduli spaces, such as SL_n(Z) and $M_g$. I will explain the general strategy of these approaches and survey results that have been obtained so far.

To give an example, I will first explain how Borel-Serre duality can be used to show that the rational cohomology of SL_n(Z) vanishes near its virtual cohomological dimension. This is based on joint work with Miller-Patzt-Sroka-Wilson and builds on results by Church-Farb-Putman. I will then put this into a more general context by giving an overview of analogous results for mapping class groups of surfaces, automorphism groups of free groups and further arithmetic groups such as SL_n(O_k) and SP_2n(Z).

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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