Geodesic
Cusps, Kleinian groups, and Eisenstein series
Forum of Mathematics, Sigma, Tome 11 (2023)

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We study the Eisenstein series associated to the full rank cusps in a complete hyperbolic manifold. We show that given a Kleinian group $\Gamma {\operatorname{\mathrm{Isom}}}^+(\mathbb H^{n+1})$, each full rank cusp corresponds to a cohomology class in $H^{n}(\Gamma , V)$, where V is either the trivial coefficient or the adjoint representation. Moreover, by computing the intertwining operator, we show that different cusps give rise to linearly independent classes. 
@article{10_1017_fms_2023_73,
     author = {Beibei Liu and Shi Wang},
     title = {Cusps, {Kleinian} groups, and {Eisenstein} series},
     journal = {Forum of Mathematics, Sigma},
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     year = {2023},
     doi = {10.1017/fms.2023.73},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.73/}
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Beibei Liu; Shi Wang. Cusps, Kleinian groups, and Eisenstein series. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.73

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