Minimum volume cusped hyperbolic three-manifolds
نویسندگان
چکیده
منابع مشابه
Minimum Volume Cusped Hyperbolic Three-manifolds
This corollary extends work of Cao and Meyerhoff who had earlier shown that m003 and m004 were the smallest volume cusped manifolds. Also, the above list agrees with the SnapPea census of one-cusped manifolds produced by Jeff Weeks ([W]), whose initial members are conjectured to be an accurate list of small-volume cupsed manifolds. Let N be a closed hyperbolic 3-manifold with simple closed geod...
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The classification of small-volume hyperbolic 3-manifolds has been an active problem for many years, ever since Thurston suggested that volume was a measure of the complexity of a hyperbolic 3-manifold. Quite recently in [GMM3] the author along with David Gabai and Robert Meyerhoff used a geometrical construction called a Mom-n structure to tackle the classification problem, and succeeded in sh...
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Let M be a complete, finite-volume, orientable hyperbolic manifold having exactly one cusp. If we assume that π1(M) has no subgroup isomorphic to a genus-2 surface group, and that either (a) dimZp H1(M ;Zp) ≥ 5 for some prime p, or (b) dimZ2 H1(M ;Z2) ≥ 4, and the subspace of H(M ;Z2) spanned by the image of the cup product H(M ;Z2) × H(M ;Z2) → H(M ;Z2) has dimension at most 1, then volM > 5.0...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2009
ISSN: 0894-0347
DOI: 10.1090/s0894-0347-09-00639-0