A hyperbolic counterpart to Rokhlin's cobordism theorem [article]

Michelle Chu, Alexander Kolpakov
2020 arXiv   pre-print
The purpose of the present paper is to prove existence of super-exponentially many compact orientable hyperbolic arithmetic n-manifolds that are geometric boundaries of compact orientable hyperbolic (n+1)-manifolds, for any n ≥ 2, thereby establishing that these classes of manifolds have the same growth rate with respect to volume as all compact orientable hyperbolic arithmetic n-manifolds. An analogous result holds for non-compact orientable hyperbolic arithmetic n-manifolds of finite volume that are geometric boundaries, for n ≥ 2.
arXiv:1905.04774v5 fatcat:xoz3iljqvnbyxjnk22x2wlxuoe