3 papers
math.GT2025
Cusp cross-section phenomena for arithmetic hyperbolic manifolds
Duncan McCoy, Connor Sell
Although every flat manifold occurs as a cusp cross-section in at least one commensurability class of arithmetic hyperbolic manifolds, it turns out that some flat manifolds have th…
math.GT2025
Cusp types of arithmetic hyperbolic manifolds
Duncan McCoy, Connor Sell
We establish necessary and sufficient conditions for determining when a flat manifold can occur as a cusp cross-section within a given commensurability class of cusped arithmetic h…
math.GT2024
Nil 3-manifolds and cusps of complex hyperbolic surfaces
Julien Paupert, Connor Sell
McReynolds showed that every compact Nil 3-manifold occurs as the cusp cross-section of some arithmetic complex hyperbolic 2-manifold. We classify which commensurability classes of…