Cohomology at infinity and the well-tempered complex

Dylan Galt; Mark McConnell

doi:10.1007/s40062-025-00385-6

Cohomology at infinity and the well-tempered complex

Dylan Galt
, Mark McConnell

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the existence of a sequence of commutative diagrams generalizing the results on cohomology at infinity described in Ash and McConnell (Duke Math J 90:549–576, 1997) to the context of the well-tempered complex introduced in McConnell and MacPherson (Computing Hecke operators for arithmetic subgroups of general linear groups, http://arxiv.org/abs/2010.06036, 2020). Our main theorem provides a method for computing in finite terms the action of Hecke operators on the cohomology of the Borel-Serre boundary for the SLn symmetric space.

Original language	English (US)
Pages (from-to)	1-21
Number of pages	21
Journal	Journal of Homotopy and Related Structures
Volume	21
Issue number	1
DOIs	https://doi.org/10.1007/s40062-025-00385-6
State	Published - Mar 2026

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

Keywords

Borel-Serre compactification
Cohomology of arithmetic groups
Hecke operators
Well-rounded retract
Well-tempered complex

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10.1007/s40062-025-00385-6

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N2 - We prove the existence of a sequence of commutative diagrams generalizing the results on cohomology at infinity described in Ash and McConnell (Duke Math J 90:549–576, 1997) to the context of the well-tempered complex introduced in McConnell and MacPherson (Computing Hecke operators for arithmetic subgroups of general linear groups, http://arxiv.org/abs/2010.06036, 2020). Our main theorem provides a method for computing in finite terms the action of Hecke operators on the cohomology of the Borel-Serre boundary for the SLn symmetric space.

AB - We prove the existence of a sequence of commutative diagrams generalizing the results on cohomology at infinity described in Ash and McConnell (Duke Math J 90:549–576, 1997) to the context of the well-tempered complex introduced in McConnell and MacPherson (Computing Hecke operators for arithmetic subgroups of general linear groups, http://arxiv.org/abs/2010.06036, 2020). Our main theorem provides a method for computing in finite terms the action of Hecke operators on the cohomology of the Borel-Serre boundary for the SLn symmetric space.

KW - Borel-Serre compactification

KW - Cohomology of arithmetic groups

KW - Hecke operators

KW - Well-rounded retract

KW - Well-tempered complex

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Cohomology at infinity and the well-tempered complex

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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