A Hyperbolic Counterpart to Rokhlin's Cobordism Theorem. (9th July 2020)

• Record Type: Journal Article
• Authors: Chu, Michelle; Kolpakov, Alexander
• Is Part Of: International mathematics research notices. Volume 2022:Number 4(2022)
• Page Start: 2460
• Page End: 2483
• Publication Date: 2020-07-09
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnaa158
• Languages: English
• ISSNs: 1073-7928

Abstract

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 $n \geq 2$ .