The Weeks manifold is a closed orientable hyperbolic 3-manifold
of volume approximately 0.942707. It can be
obtained by Dehn filling the two cusps of the Whitehead link complement with suitable slopes. The
manifold is also called the Fomenko-Matveev-Weeks manifold.
The Weeks manifold has the smallest volume among all closed orientable hyperbolic 3-manifolds
(Gabai et al. 2009). Its first homology group
is 
.
See also
Hyperbolic Geometry,
Hyperbolic Volume,
Manifold,
Whitehead
Link
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References
Gabai, D.; Meyerhoff, R.; and Milley, P. "Minimum Volume Cusped Hyperbolic Three-Manifolds." J. Amer. Math. Soc. 22, 1157-1215,
2009. https://doi.org/10.1090/S0894-0347-09-00639-0.
Cite this as:
Weisstein, Eric W. "Weeks Manifold." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WeeksManifold.html
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