Cocompact cubulations of mixed 3-manifolds

Flat Lorentz 3 - manifolds and cocompact

Cubulations of Symplectic 4-manifolds

Here is a construction of a simplicial decomposition of a symplectic 4-manifold into simplices which are of a standard form up to symplectomorphism. It is clear that much of the construction generalizes to higher dimensions. A standard closed 4-simplex is a closed subset of C with coordinates z,w of the form ∆ = {(z, w)|z ∈ S1, w ∈ S2} where S1 and S2 are squares in the z and w planes. The simp...

Flat Lorentz 3-manifolds and cocompact Fuchsian groups

Mess deduces this result as part of a general theory of domains of dependence in constant curvature Lorentzian 3-manifolds. We give an alternate proof, using an invariant introduced by Margulis [18, 19] and Teichmüller theory. We thank Scott Wolpert for helpful conversations concerning Teichmüller theory. We also wish to thank Paul Igodt and the Algebra Research Group at the Katholieke Universi...

Holography and the Geometry of Certain Convex Cocompact Hyperbolic 3-Manifolds

Applying the idea of AdS/CFT correspondence, Krasnov [Kra00] studied a class of convex cocompact hyperbolic 3-manifolds. In physics literature they are known as Euclidean BTZ black holes. Mathematically they can be described as H/Γ, where Γ ⊂ PSL(2,C) is a Schottky group. His main result, roughly speaking, identifies the renormalized volume of such a manifold with the action for the Liouville t...

Mixed 3–manifolds Are Virtually Special

LetM be a compact oriented irreducible 3–manifold which is neither a graph manifold nor a hyperbolic manifold. We prove that π1M is virtually special.