Geodesic planes in geometrically finite acylindrical -manifolds

Abstract Let M be a geometrically finite acylindrical hyperbolic $3$ -manifold and let $M^*$ denote the interior of convex core . We show that any geodesic plane in is either closed or dense, there are only countably many planes These results were obtained by McMullen, Mohammadi Oh [Geodesic 3-manifolds. Invent. Math. 209 (2017), 425–461; Geodesic an 3-manifold. Duke J. , to appear, Preprint 2018, arXiv:1802.03853] when cocompact. As corollary, we obtain covers arithmetic $M_0$ topological behavior governed corresponding construct counterexample this phenomenon non-arithmetic.