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17 papers · 1 filter
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…
Virtual Crossing Number and the Arrow Polynomial
H. A. Dye, Louis H. Kauffman
We introduce a new polynomial invariant of virtual knots and links and use this invariant to compute a lower bound on the virtual crossing number and the minimal surface genus.
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…
Characteristic classes for Riemannian foliations
Steven Hurder
The purpose of this paper is to both survey and offer some new results on the non-triviality of the characteristic classes of Riemannian foliations. We give examples where the prim…
On the doubled tetrus
Jason DeBlois
The tetrus is a sort of big brother to the tripus, W.P. Thurston's example of a compact hyperbolic 3-manifold with totally geodesic boundary. We describe a sixfold cover of the dou…