All nil 3-manifolds are cusps of complex hyperbolic 2-orbifolds

All at Manifolds Are Cusps of Hyperbolic Orbifolds

All flat manifolds are cusps of hyperbolic orbifolds

We show that all closed flat n-manifolds are diffeomorphic to a cusp cross-section in a finite volume hyperbolic n + 1-orbifold.

Peripheral separability and cusps of arithmetic hyperbolic orbifolds

For X = R , C , or H , it is well known that cusp cross-sections of finite volume X –hyperbolic (n + 1)–orbifolds are flat n–orbifolds or almost flat orbifolds modelled on the (2n + 1)–dimensional Heisenberg group N2n+1 or the (4n + 3)–dimensional quaternionic Heisenberg group N4n+3(H). We give a necessary and sufficient condition for such manifolds to be diffeomorphic to a cusp cross-section o...

Volumes of Picard modular surfaces

We show that the conjectural cusped complex hyperbolic 2-orbifolds of minimal volume are the two smallest arithmetic complex hyperbolic 2orbifolds. We then show that every arithmetic cusped complex hyperbolic 2-manifold of minimal volume covers one of these two orbifolds. We also give all minimal volume manifolds that simultaneously cover both minimal orbifolds.

Cusps of Minimal Non-compact Arithmetic Hyperbolic 3-orbifolds

In this paper we count the number of cusps of minimal non-compact finite volume arithmetic hyperbolic 3-orbifolds. We show that for each N , the orbifolds of this kind which have exactly N cusps lie in a finite set of commensurability classes, but either an empty or an infinite number of isometry classes.