Cohomology of congruence subgroups of SL(4,Z)

Avner Ash; Paul E. Gunnells; Mark McConnell

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arXiv · math/0003219

Cohomology of congruence subgroups of SL(4,Z)

Avner Ash·Paul E. Gunnells·Mark McConnell

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Abstract

Let $N>1$ be an integer, and let $Γ= Γ_0 (N) \subset \SL_4 (\Z)$ be the subgroup of matrices with bottom row congruent to $(0,0,0,*)\mod N$. We compute $H^5 (Γ; \C) $ for a range of $N$, and compute the action of some Hecke operators on many of these groups. We relate the classes we find to classes coming from the boundary of the Borel-Serre compactification, to Eisenstein series, and to classical holomorphic modular forms of weights 2 and 4.

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BibTeX RIS

Avner Ash, Paul E. Gunnells, Mark McConnell. 2000-03-30. Cohomology of congruence subgroups of SL(4,Z). https://arxiv.org/abs/math/0003219

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