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Title: 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 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.  more » « less
Award ID(s):
1900101
PAR ID:
10339880
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Ergodic Theory and Dynamical Systems
Volume:
42
Issue:
2
ISSN:
0143-3857
Page Range / eLocation ID:
514 to 553
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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