Cohomology of congruence subgroups of SL(4,Z) II

By A. Ash, Paul E. Gunnells, Mark McConnell. 2002

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Abstract In a previous paper [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL 4 ( Z ) , J. Number Theory 94 (2002) 181–212] we computed cohomology groups H 5 ( Γ 0 ( N ) , C ) , where Γ 0 ( N ) is a certain congruence subgroup of SL ( 4 , Z ) , for a range of levels N. In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and additional boundary phenomena found since the publication of [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL 4 ( Z ) , J. Number Theory 94 (2002) 181–212]. The cuspidal cohomology classes in this paper are the first cuspforms for GL ( 4 ) concretely constructed in terms of Betti cohomology.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1f3846792d707450bd80582281935f7cd014c596