Weeks Manifold
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High Quality Content by WIKIPEDIA articles! 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 .9427... and Gabai, Meyerhoff & Milley (2009) showed that it has the smallest volume of any 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 f...
High Quality Content by WIKIPEDIA articles! 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 .9427... and Gabai, Meyerhoff & Milley (2009) showed that it has the smallest volume of any 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: frac{3 cdot23^{3/2}zeta_k(2)}{4pi^4}, where k is the number field generated by satisfying 3 + 1 = 0 and k is the Dedekind zeta function of k (Chinburg, 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.
