Cusps of arithmetic orbifolds

2006/06/22 by D. B. McReynolds, McReynolds, D. B.
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.math/0606571

Abstract

This thesis investigates cusp cross-sections of arithmetic real, complex, and quaternionic hyperbolic n--orbifolds. We give a smooth classification of these submanifolds and analyze their induced geometry. One of the primary tools is a new subgroup separability result for general arithmetic lattices.

Citations

• The Geometries of 3-Manifolds
• Arithmetic Subgroups of Algebraic Groups

Related

• Cusp types of arithmetic hyperbolic manifolds
• Cusp cross-section phenomena for arithmetic hyperbolic manifolds
• Subspace stabilisers in hyperbolic lattices
• The non-arithmetic cusped hyperbolic 3-orbifold of minimal volume
• A note on strong geometric isolation in 3-orbifolds