A Hyperbolic Counterpart to Rokhlin's Cobordism Theorem

Michelle Chu, Alexander Kolpakov

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2460-2483
Number of pages24
JournalInternational Mathematics Research Notices
Issue number4
StatePublished - Feb 1 2022
Externally publishedYes

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