Cohomology at Infinity and the Well-Tempered Complex

Dylan Galt; Mark McConnell

Cohomology at Infinity and the Well-Tempered Complex

Number Theory 2025-10-21 v2

Authors: Dylan Galt , Mark McConnell

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 $\Gamma$ of the special linear group $SL_n$ .

Keywords

cohomology well-tempered complex borel-serre boundary hecke operators equivariant cohomology arithmetic subgroup special linear group

Cite

@article{arxiv.2301.10817,
  title  = {Cohomology at Infinity and the Well-Tempered Complex},
  author = {Dylan Galt and Mark McConnell},
  journal= {arXiv preprint arXiv:2301.10817},
  year   = {2025}
}

Comments

Minor typos corrected; final version appearing in Journal of Homotopy Theory and Related Structures

Cohomology at Infinity and the Well-Tempered Complex

Abstract

Keywords

Cite

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