Abstract
For a complete hyperbolic three manifold $M$, we consider the representations of $\pi_{1}(M)$ obtained by composing a lift of the holonomy with complex finite dimensional representations of $\mathrm{SL}(2,\mathbf{C})$. We prove a vanishing result for the cohomology of $M$ with coefficients twisted by these representations, using techniques of Matsushima--Murakami. We give some applications to local rigidity.
Citation
Pere Menal-Ferrer. Joan Porti. "Twisted cohomology for hyperbolic three manifolds." Osaka J. Math. 49 (3) 741 - 769, September 2012.
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