On the Cohomology of GL2 and SL2 over Imaginary Quadratic Fields

Gangl, Herbert; Gunnells, Paul E.; Hanke, Jonathan; Yasaki, Dan

Abstract

We report on computations of the cohomology of (Formula presented.) and (Formula presented.), where D < 0 is a fundamental discriminant. These computations go well beyond earlier results of Vogtmann and Scheutzow. We use the technique of homology of Voronoi complexes, and our computations recover the integral cohomology away from the primes 2, 3. We observed exponential growth in the torsion subgroup of H 2 as (Formula presented.) increases, and compared our data to bounds of Rohlfs.

Citation

Gangl, H., Gunnells, P. E., Hanke, J., & Yasaki, D. (online). On the Cohomology of GL2 and SL2 over Imaginary Quadratic Fields. Experimental Mathematics, https://doi.org/10.1080/10586458.2024.2379797

• Journal Article Type: Article
• Acceptance Date: Aug 20, 2024
• Online Publication Date: Sep 1, 2024
• Deposit Date: Sep 4, 2024
• Publicly Available Date: Sep 5, 2024
• Journal: Experimental Mathematics
• Print ISSN: 1058-6458
• Electronic ISSN: 1944-950X
• Publisher: Taylor and Francis Group
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1080/10586458.2024.2379797
• Public URL: https://durham-repository.worktribe.com/output/2786213