4 papers
Hyperbolic volume, Heegaard genus and ranks of groups
Peter B Shalen
Some conjectures about Heegaard genera and ranks of fundamental groups of 3-manifolds are formulated, and it is shown that they imply new statements about hyperbolic volume.
Volume and topology of bounded and closed hyperbolic 3-manifolds
Jason DeBlois, Peter B. Shalen
Let N be a compact, orientable hyperbolic 3-manifold with connected, totally geodesic boundary of genus 2. If N has Heegaard genus at least 5, then its volume is greater than 6.89.…
Betti numbers and injectivity radii
Marc Culler, Peter B. Shalen
We give lower bounds on the maximal injectivity radius for a closed orientable hyperbolic 3-manifold M with first Betti number 2, under some additional topological hypotheses. A co…
Incompressible surfaces, hyperbolic volume, Heegaard genus and homology
Marc Culler, Jason DeBlois, Peter B. Shalen
We show that if M is a complete, finite-volume, hyperbolic 3-manifold having exactly one cusp, and if H_1(M;Z_2) has dimension at least 6, then M has volume greater than 5.06. We a…