A hyperbolic counterpart to Rokhlin's cobordism theorem release_5vhdawayzzaxrp5bv6wekxx25e

by Michelle Chu, Alexander Kolpakov

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2019  

Abstract

The purpose of the present note 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 each 2 ≤ n ≤ 8, thereby establishing that these classes of manifolds have the same growth rate with respect to volume as all compact orientable hyperbolic arithmetic n-manifolds, for each 2 ≤ n ≤ 8, respectively. An analogous result holds for non-compact orientable hyperbolic n-manifolds of finite volume that are geometric boundaries, for 2 ≤ n ≤ 19 and n=21.
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Date   2019-05-12
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arXiv  1905.04774v1
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