Work

On the Cohomology of GL 2 and SL 2 over Imaginary Quadratic Fields

Year: 2024

Type: article

Abstract: We report on computations of the cohomology of GL2(OD) and SL2(OD), 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 |D| increases, and compared our data to bounds of Rohlfs.

Source: Experimental Mathematics

DOI: 10.1080/10586458.2024.2379797

Authors: Herbert Gangl, Paul E. Gunnells, Jonathan Hanke, Dan Yasaki

Institutions: Durham University, University of Massachusetts Amherst, University of Massachusetts System, Princeton University, University of North Carolina at Greensboro

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, American Institute of Mathematics

Awards: Multiple Dirichlet series, Whittaker functions, and the cohomology of arithmetic groups, Problems in arithmetic groups and multiple Dirichlet series.