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Finiteness of Maximal Geodesic Submanifolds in Hyperbolic Hybrids
- Publication Year :
- 2018
-
Abstract
- We show that large classes of non-arithmetic hyperbolic $n$-manifolds, including the hybrids introduced by Gromov and Piatetski-Shapiro and many of their generalizations, have only finitely many finite-volume immersed totally geodesic hypersurfaces. In higher codimension, we prove finiteness for geodesic submanifolds of dimension at least $2$ that are maximal, i.e., not properly contained in a proper geodesic submanifold of the ambient $n$-manifold. The proof is a mix of structure theory for arithmetic groups, dynamics, and geometry in negative curvature.<br />Comment: v2. Improved writing, improved Theorem 1.3, other results unchanged. 31 pages, 9 figures. v1. 28 pages, 9 figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1802.04619
- Document Type :
- Working Paper