On the Cohomology of GL <sub>2</sub> and SL <sub>2</sub> over Imaginary Quadratic Fields
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.
Authors
- Herbert Gangl (ORCID: https://orcid.org/0000-0001-7785-263X)
- Paul E. Gunnells (ORCID: https://orcid.org/0000-0002-2742-3025)
- Jonathan Hanke
- Dan Yasaki (ORCID: https://orcid.org/0000-0001-8179-8197)
Institutions
- University of North Carolina at Greensboro (US)
- University of Massachusetts Amherst (US)
- Princeton Public Schools (US)
Publication Details
- Journal
- Experimental Mathematics
- Published
- 2024-09-01
- DOI
- https://doi.org/10.1080/10586458.2024.2379797
- Primary Topic
- Advanced Algebra and Geometry
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- American Institute of Mathematics