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- Weeks_manifold abstract "In mathematics, the Weeks manifold, sometimes called the Fomenko–Matveev–Weeks manifold, is a closed hyperbolic 3-manifold obtained by (5, 2) and (5, 1) Dehn surgeries on the Whitehead link. It has volume approximately equal to 0.9427... and Gabai, Meyerhoff & Milley (2009) showed that it has the smallest volume of any closed orientable hyperbolic 3-manifold. The manifold was independently discovered by Weeks (1985) and Matveev & Fomenko (1988). Since the Weeks manifold is an arithmetic hyperbolic 3-manifold, its volume can be computed using its arithmetic data and a formula due to A. Borel: where k is the number field generated by θ satisfying θ 3 − θ + 1 = 0 and ζ k is the Dedekind zeta function of k (Ted Chinburg, Eduardo Friedman & Kerry N. Jones et al. 2001)The cusped hyperbolic 3-manifold obtained by (5, 1) Dehn surgery on the Whitehead link is the so-called sibling manifold, or sister, of the figure eight knot complement. The figure eight knot's complement and its sibling have the smallest volume of any orientable, cusped hyperbolic 3-manifold. Thus the Weeks manifold can be obtained by hyperbolic Dehn surgery on one of the two smallest orientable cusped hyperbolic 3-manifolds.".
- Weeks_manifold wikiPageExternalLink item?id=ASNSP_2001_4_30_1_1_0.
- Weeks_manifold wikiPageID "4201216".
- Weeks_manifold wikiPageRevisionID "429999466".
- Weeks_manifold first "Alan W.".
- Weeks_manifold first "Eduardo".
- Weeks_manifold first "Kerry N.".
- Weeks_manifold first "Ted".
- Weeks_manifold hasPhotoCollection Weeks_manifold.
- Weeks_manifold issue "1".
- Weeks_manifold journal "Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV".
- Weeks_manifold last "Chinburg".
- Weeks_manifold last "Friedman".
- Weeks_manifold last "Jones".
- Weeks_manifold last "Reid".
- Weeks_manifold mr "1882023".
- Weeks_manifold pages "1".
- Weeks_manifold title "The arithmetic hyperbolic 3-manifold of smallest volume".
- Weeks_manifold volume "30".
- Weeks_manifold year "2001".
- Weeks_manifold zbl "1008.11015".
- Weeks_manifold subject Category:3-manifolds.
- Weeks_manifold subject Category:Hyperbolic_geometry.
- Weeks_manifold comment "In mathematics, the Weeks manifold, sometimes called the Fomenko–Matveev–Weeks manifold, is a closed hyperbolic 3-manifold obtained by (5, 2) and (5, 1) Dehn surgeries on the Whitehead link. It has volume approximately equal to 0.9427... and Gabai, Meyerhoff & Milley (2009) showed that it has the smallest volume of any closed orientable hyperbolic 3-manifold. The manifold was independently discovered by Weeks (1985) and Matveev & Fomenko (1988).".
- Weeks_manifold label "Weeks manifold".
- Weeks_manifold sameAs m.0bpn_c.
- Weeks_manifold sameAs Q7979541.
- Weeks_manifold sameAs Q7979541.
- Weeks_manifold wasDerivedFrom Weeks_manifold?oldid=429999466.
- Weeks_manifold isPrimaryTopicOf Weeks_manifold.