A Hyperbolic Counterpart to Rokhlin's Cobordism Theorem. (9th July 2020) - Chu, Michelle
Abstract: 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 $n \geq 2$, 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 $n \geq 2$ .