Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 8, Number 1 (2008), 343-379.
Volume and homology of one-cusped hyperbolic $3$–manifolds
Let be a complete, finite-volume, orientable hyperbolic manifold having exactly one cusp. If we assume that has no subgroup isomorphic to a genus– surface group and that either (a) for some prime , or (b) , and the subspace of spanned by the image of the cup product has dimension at most , then If we assume that and that the compact core of contains a genus– closed incompressible surface, then Furthermore, if we assume only that , then
Algebr. Geom. Topol., Volume 8, Number 1 (2008), 343-379.
Received: 24 August 2007
Revised: 3 February 2007
Accepted: 17 December 2007
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57M27: Invariants of knots and 3-manifolds
Culler, Marc; Shalen, Peter B. Volume and homology of one-cusped hyperbolic $3$–manifolds. Algebr. Geom. Topol. 8 (2008), no. 1, 343--379. doi:10.2140/agt.2008.8.343. https://projecteuclid.org/euclid.agt/1513796816