Volume and homology of one-cusped hyperbolic 3–manifolds

Culler, Marc¹ ; Shalen, Peter B¹

¹Department of Mathematics (M/C 249), University of Illinois at Chicago, 851 S Morgan St, Chicago, IL 60607-7045

Algebraic and Geometric Topology, Tome 8 (2008) no. 1, pp. 343-379

Résumé

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) dimℤpH1(M; ℤp) ≥ 5 for some prime p, or (b) dimℤ2H1(M; ℤ2) ≥ 4, and the subspace of H2(M; ℤ2) spanned by the image of the cup product H1(M; ℤ2) × H1(M; ℤ2) → H2(M; ℤ2) has dimension at most 1, then volM > 5.06. If we assume that dimℤ2H1(M; ℤ2) ≥ 7 and that the compact core N of M contains a genus–2 closed incompressible surface, then volM > 5.06. Furthermore, if we assume only that dimℤ2H1(M; ℤ2) ≥ 7, then volM > 3.66.

Détail

DOI : 10.2140/agt.2008.8.343

Keywords: hyperbolic manifold, cusp, volume, homology, Dehn filling

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