Compact hyperbolic 4-manifolds of small volume

Conder, Marston; Maclachlan, Colin

doi:10.1090/S0002-9939-05-07634-3

Compact hyperbolic 4-manifolds of small volume
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by Marston Conder and Colin Maclachlan

Proc. Amer. Math. Soc. 133 (2005), 2469-2476

DOI: https://doi.org/10.1090/S0002-9939-05-07634-3

Published electronically: March 14, 2005

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Abstract:

We prove the existence of a compact non-orientable hyperbolic 4-manifold of volume $32\pi ^{2}/3$ and a compact orientable hyperbolic 4-manifold of volume $64\pi ^{2}/3$, obtainable from torsion-free subgroups of small index in the Coxeter group $[5,3,3,3]$. At the time of writing these are the smallest volumes of any known compact hyperbolic 4-manifolds.

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