ar X iv : 0 70 7 . 43 00 v 1 [ m at h . G T ] 2 9 Ju l 2 00 7 VOLUME AND HOMOLOGY OF ONE - CUSPED HYPERBOLIC 3 - MANIFOLDS
نویسنده
چکیده
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 > 5.06. If we assume that dimZ2 H1(M ;Z2) ≥ 11, then volM > 3.66; and furthermore, either volM > 5.06, or the compact core N of M contains a genus-2 connected incompressible surface S of a special type (S is the frontier of some book of I-bundles, possibly with a hollow binding, contained in N).
منابع مشابه
2 3 A ug 2 00 7 VOLUME AND HOMOLOGY OF ONE - CUSPED HYPERBOLIC 3 - MANIFOLDS
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....
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