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A hyperbolic counterpart to Rokhlin's cobordism theorem
release_5vhdawayzzaxrp5bv6wekxx25e
by
Michelle Chu, Alexander Kolpakov
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as a article
.
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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1905.04774v1
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