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