The mod 2 cohomology rings of SL2 of the imaginary quadratic integers

• Ethan Berkove ^[1] ; Alexander D. Rahm ^[2]
  1. [1] Lafayette College

     Lafayette College

     City of Easton, Estados Unidos

     
  2. [2] National University of Ireland

     National University of Ireland

     Irlanda

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 220, Nº 3 (March 2016), 2016, págs. 944-975
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.08.002
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• Resumen

  • We establish general dimension formulae for the second page of the equivariant spectral sequence of the action of the SL2 groups over imaginary quadratic integers on their associated symmetric space. By way of doing this, 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.