Cusps, Kleinian groups and Eisenstein series

Abstract

We study the Eisenstein series associated to the full rank cusps in a complete hyperbolic manifold. We show that given a Kleinian group $\Gamma <\text{Isom}({\mathbb{H}}^{n+1})$, 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.

This is the final version accepted for publication in Forum Math. Sigma

References in corpus (1)

• Hyperbolic manifolds that fiber algebraically up to dimension 8