Finiteness of maximal geodesic submanifolds in hyperbolic hybrids
David Fisher
Indiana University, Bloomington, USAJean-François Lafont
Ohio State University, Columbus, USANicholas Miller
University of California at Berkeley, USAMatthew Stover
Temple University, Philadelphia, USA
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Abstract
We show that large classes of non-arithmetic hyperbolic -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 that are maximal, i.e., not properly contained in a proper geodesic submanifold of the ambient -manifold. The proof is a mix of structure theory for arithmetic groups, dynamics, and geometry in negative curvature.
Cite this article
David Fisher, Jean-François Lafont, Nicholas Miller, Matthew Stover, Finiteness of maximal geodesic submanifolds in hyperbolic hybrids. J. Eur. Math. Soc. 23 (2021), no. 11, pp. 3591–3623
DOI 10.4171/JEMS/1077