Geodesic
Minimum volume cusped hyperbolic three-manifolds
Gabai, David1 ; Meyerhoff, Robert2 ; Milley, Peter3
1 Department of Mathematics, Princeton University, Princeton, New Jersey 08544
2 Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
3 Department of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
Journal of the American Mathematical Society, Tome 22 (2009) no. 4, pp. 1157-1215

Voir la notice de l'article provenant de la source American Mathematical Society

This paper is the second in a series whose goal is to understand the structure of low-volume complete orientable hyperbolic $3$-manifolds. Using Mom technology, we prove that any one-cusped hyperbolic $3$-manifold with volume $\le 2.848$ can be obtained by a Dehn filling on one of $21$ cusped hyperbolic $3$-manifolds. We also show how this result can be used to construct a complete list of all one-cusped hyperbolic $3$-manifolds with volume $\le 2.848$ and all closed hyperbolic $3$-manifolds with volume $\le 0.943$. In particular, the Weeks manifold is the unique smallest volume closed orientable hyperbolic $3$-manifold.
DOI : 10.1090/S0894-0347-09-00639-0

Gabai, David 1 ; Meyerhoff, Robert 2 ; Milley, Peter 3

1 Department of Mathematics, Princeton University, Princeton, New Jersey 08544
2 Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
3 Department of Mathematics and Statistics, University of Melbourne, Melbourne, Australia 
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Gabai, David; Meyerhoff, Robert; Milley, Peter. Minimum volume cusped hyperbolic three-manifolds. Journal of the American Mathematical Society, Tome 22 (2009) no. 4, pp. 1157-1215. doi: 10.1090/S0894-0347-09-00639-0

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