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Journal Article

#### Boundary and Eisenstein cohomology of SL_{3}(Z)

##### MPS-Authors

##### External Resource

https://doi.org/10.1007/s00208-020-01976-9

(Publisher version)

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##### Fulltext (public)

1812.03734.pdf

(Preprint), 391KB

Bajpai-Harder-Horozov-Moya Giusti_Boundary and Eisenstein cohomology_2020.pdf

(Publisher version), 480KB

##### Supplementary Material (public)

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##### Citation

Bajpai, J., Harder, G., Horozov, I. E., & Moya Giusti, M. V. (2020). Boundary and
Eisenstein cohomology of SL_{3}(Z).* Mathematische Annalen,* *377*(1-2),
199-247. doi:10.1007/s00208-020-01976-9.

Cite as: https://hdl.handle.net/21.11116/0000-0006-7C97-5

##### Abstract

In this article, several cohomology spaces associated to the arithmetic groups $\mathrm{SL}_3(\mathbb{Z})$ and $\mathrm{GL}_3(\mathbb{Z})$ with

coefficients in any highest weight representation $\mathcal{M}_\lambda$ have

been computed, where $\lambda$ denotes their highest weight. Consequently, we

obtain detailed information of their Eisenstein cohomology with coefficients in

$\mathcal{M}_\lambda$. When $\mathcal{M}_\lambda$ is not self dual, the

Eisenstein cohomology coincides with the cohomology of the underlying arithmetic group with coefficients in $\mathcal{M}_\lambda$. In particular, for such a large class of representations we can explicitly describe the cohomology of these two arithmetic groups. We accomplish this by studying the cohomology of the boundary of the Borel-Serre compactification and their Euler

characteristic with coefficients in $\mathcal{M}_\lambda$. At the end, we

employ our study to discuss the existence of ghost classes.

coefficients in any highest weight representation $\mathcal{M}_\lambda$ have

been computed, where $\lambda$ denotes their highest weight. Consequently, we

obtain detailed information of their Eisenstein cohomology with coefficients in

$\mathcal{M}_\lambda$. When $\mathcal{M}_\lambda$ is not self dual, the

Eisenstein cohomology coincides with the cohomology of the underlying arithmetic group with coefficients in $\mathcal{M}_\lambda$. In particular, for such a large class of representations we can explicitly describe the cohomology of these two arithmetic groups. We accomplish this by studying the cohomology of the boundary of the Borel-Serre compactification and their Euler

characteristic with coefficients in $\mathcal{M}_\lambda$. At the end, we

employ our study to discuss the existence of ghost classes.