34 citations · 94 across the 12 of their papers we have counts for
12 papers
Orderability and Dehn filling
Marc Culler, Nathan M. Dunfield
Motivated by conjectures relating group orderability, Floer homology, and taut foliations, we discuss a systematic and broadly applicable technique for constructing left-orders on…
Margulis numbers for Haken manifolds
Marc Culler, Peter B. Shalen
For every closed hyperbolic Haken 3-manifold and, more generally, for any hyperbolic 3-manifold M which is homeomorphic to the interior of a Haken manifold, the number 0.286 is a M…
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…
Four-free groups and hyperbolic geometry
Marc Culler, Peter B. Shalen
We give new information about the geometry of closed, orientable hyperbolic 3-manifolds with 4-free fundamental group. As an application we show that such a manifold has volume gre…
Volume and homology of one-cusped hyperbolic 3-manifolds
Marc Culler, Peter B. Shalen
Let M be a complete, finite-volume, orientable hyperbolic manifold having exactly one cusp. If we assume that pi_1(M) has no subgroup isomorphic to a genus-2 surface group, and tha…