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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Compact hyperbolic 4-manifolds of small volume


Authors: Marston Conder and Colin Maclachlan
Journal: Proc. Amer. Math. Soc. 133 (2005), 2469-2476
MSC (2000): Primary 57M50, 20F55; Secondary 51M20, 20B40
Published electronically: March 14, 2005
MathSciNet review: 2138890
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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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Additional Information

Marston Conder
Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019 Auckland, New Zealand
Email: m.conder@auckland.ac.nz

Colin Maclachlan
Affiliation: Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE, Scotland, United Kingdom
Email: c.maclachlan@maths.abdn.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07634-3
PII: S 0002-9939(05)07634-3
Keywords: 4-manifolds, finitely-presented groups
Received by editor(s): August 29, 2003
Published electronically: March 14, 2005
Additional Notes: This research was supported by grants from the N.Z. Marsden Fund (grant no. UOA 124) and the N.Z. Centres of Research Excellence Fund (grant no. UOA 201)
Communicated by: Linda Keen
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.