The mod 2 cohomology rings of SL_2 of the imaginary quadratic integers

2015/07/22 by Ethan Berkove, Berkove, Ethan, Alexander Rahm +1
Mathematics · #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT

paper · pdf · doi:10.48550/arxiv.1507.06144

Version post-print corrigeant de petits erreurs concernant l'observation qui se réfère sur l'appendice, Journal of Pure and Applied Algebra, Elsevier, 2015, Accepted for publication on July 21, 2015

arxiv created 2016/08/22 · arxiv updated 2016/08/23

Abstract

We establish general dimension formulae for the second page of the equivariant spectral sequence of the action of the SL_2 groups over imaginary quadratic integers on their associated symmetric space. On the way, we extend the torsion subcomplex reduction technique to cases where the kernel of the group action is nontrivial. Using the equivariant and Lyndon-Hochschild-Serre spectral sequences, we investigate the second page differentials and show how to obtain the mod 2 cohomology rings of our groups from this information.

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