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0111 · Nov 200319922001200920172026
5 results for Vol3

Authors find no positive spun triangulations for certain hyperbolic 3-manifolds.

problem Finding positive spun triangulations for hyperbolic 3-manifolds.
method Using Choi's result, they provide examples of closed hyperbolic 3-manifolds and geodesics without positive spun ideal triangulations.
result They provide evidence for the conjecture that Vol3 has no positive spun ideal triangulation for any choice of geodesic.

We correct and complete a conjecture of D. Gabai, R. Meyerhoff and N. Thurston on the classification and properties of thin tubed closed hyperbolic 3-manifolds. We additionally show that if N is a closed hyperbolic 3-manifold, then either N=Vol3 or N contains a closed geodesic that is the core of an embedded tube of ra…

2013-05-20abs ↗pdf ↗

A closed hyperbolic 3-manifold is exceptional if its shortest geodesic does not have an embedded tube of radius ln(3)/2\ln(3)/2. D. Gabai, R. Meyerhoff and N. Thurston identified seven families of exceptional manifolds in their proof of the homotopy rigidity theorem. They identified the hyperbolic manifold known as Vol3 in …

2003-11-21abs ↗pdf ↗

New lattices in higher rank contain a fixed 3-manifold group with increasing systole.

problem Finding lattices with a fixed 3-manifold group and large systole.
method Constructing arithmetic lattices in SL(8,R)SL(8,\mathbb{R}) with specific properties.
result Existence of lattices with large systole containing a fixed 3-manifold group.