Cusps, Kleinian groups, and Eisenstein series

Abstract

Abstract 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.