Seminar

Postdoc day, Seminar 4: On the high-dimensional rational cohomology of special linear groups

Higher algebraic structures in algebra, topology and geometry

21 January 15:50 - 16:20

Robin Sroka - McMaster University

Work of Borel--Serre implies that the rational cohomology of $\operatorname{SL}_n(\mathbb{Z})$ satisfies a duality property, which is analogous to Poincaré duality for manifolds. In particular, the rational cohomology of $\operatorname{SL}_n(\mathbb{Z})$ vanishes in all degrees above its virtual cohomological dimension $v_n = {n \choose 2}$. Surprisingly, the highest two possibly non-trivial rational cohomology groups also vanish, if $n \geq 3$. In the top-degree $v_n$ this is a result of Lee--Szczarba and in codimension one $v_n - 1$ a theorem of Church--Putman. In this talk, I will discuss work in progress with Brück--Miller--Patzt--Wilson on the rational cohomology of $\operatorname{SL}_n(\mathbb{Z})$ in codimension two $v_n - 2$.

 

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Organizers
Gregory Arone
Stockholm University
Tilman Bauer
KTH Royal Institute of Technology
Alexander Berglund
Stockholm University
Søren Galatius
University of Copenhagen
Jesper Grodal,
University of Copenhagen
Thomas Kragh
Uppsala University

Program
Contact

Alexander Berglund

alexb@math.su.se

Søren Galatius

galatius@math.ku.dk

Thomas Kragh

thomas.kragh@math.uu.se

Other
information

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