Cohomology at Infinity and the Well-Tempered Complex

2023/01/25 by Dylan Galt, Galt, Dylan, M. McConnell +1
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2301.10817

openalex publication_date 2023/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of a sequence of commutative diagrams generalizing existing results on the cohomology of the Borel-Serre boundary and well-rounded retract to the context of the well-tempered complex. Our main theorem provides a method for computing in finite terms the action of Hecke operators on the equivariant cohomology of an arithmetic subgroup Γ of the special linear group SL_n.

Related

• Computing Hecke Operators for Arithmetic Subgroups of General Linear Groups
• Computing Hecke operators for arithmetic subgroups of Sp₄
• Cohomology at infinity and the well-rounded retract for general Linear Groups
• Hecke Operators on Stable Cohomology
• Introductory computations in the cohomology of arithmetic groups