Excision in equivariant cohomology with emphasis on SL_2 over imaginary quadratic integers

Ethan Berkove (1) , Alexander D. Rahm (2)

1 Mathematics Department, Lafayette College
2 NUIG - Department of Mathematics

We extend the Torsion Sub-complex Reduction technique to the case where the kernel of a group action is non-trivial. For this purpose, we excise the non-central torsion sub-complex from the equivariant spectral sequence. This new method of excision in equivariant cohomology is elaborated in a general setting. We demonstrate the power of the method by establishing 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.

Mots clés: Cohomology of arithmetic groups

Domaines: K-théorie et homologie [math.KT]

Ethan Berkove, Alexander D. Rahm. Excision in equivariant cohomology with emphasis on SL_2 over imaginary quadratic integers. 2012. ⟨hal-00769261v1⟩