Cohomology at Infinity and the Well-Tempered Complex

Dylan Galt; Mark McConnell

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arXiv · 2301.10817

Cohomology at Infinity and the Well-Tempered Complex

Dylan Galt·Mark McConnell

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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 $SL_n$.

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Dylan Galt, Mark McConnell. 2023-01-25. Cohomology at Infinity and the Well-Tempered Complex. https://arxiv.org/abs/2301.10817

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