5 papers · 1 filter
A note on an effective characterization of covers with an application to higher rank representations
Tarik Aougab, Max Lahn, Marissa Loving +1
In this note we prove an effective characterization of when two finite-degree covers of a connected, orientable surface of negative Euler characteristic are isomorphic in terms of…
Arithmeticity, Superrigidity, and Totally Geodesic Submanifolds
Uri Bader, David Fisher, Nick Miller +1
Let be a lattice in . We prove that if the associated locally symmetric space contains infinitely many maximal totally geodesic subspaces of dimension at l…
On the genus of congruence surfaces from maximal orders
Eric Albers, Nicholas Miller
In this paper, we investigate a question of Breuillard and Reid concerning which genera can be obtained by closed congruence surfaces. Specifically, we study a smaller set of objec…
Effective virtual and residual properties of some arithmetic hyperbolic 3-manifolds
Jason DeBlois, Nicholas Miller, Priyam Patel
We give an effective upper bound, for certain arithmetic hyperbolic 3-manifold groups obtained from a quadratic form construction, on the minimal index of a subgroup that embeds in…
Areas of totally geodesic surfaces of hyperbolic 3-orbifolds
Benjamin Linowitz, D. B. McReynolds, Nicholas Miller
The geodesic length spectrum of a complete, finite volume, hyperbolic 3-orbifold M is a fundamental invariant of the topology of M via Mostow-Prasad Rigidity. Motivated by this, th…