We show that a graph manifold which is a Z-homology 3-sphere not homeomorphic to either S or Σ(2, 3, 5) admits a horizontal foliation. This combines with known results to show that the conditions of not being an L-space, of having a left-orderable fundamental group, and of admitting a co-oriented taut foliation, are equivalent for graph manifold Z-homology 3-spheres.

Let F be a compact Hausdorff foliation on a compact manifold. Let E 2 = ⊕{E 2 : p > 0, q ≥ 0} be the subalgebra of cohomology classes with positive transverse degree in the E2 term of the spectral sequence of the foliation. We prove that the saturated transverse Lusternik-Schnirelmann category of F is bounded below by the length of the cup product in E 2 . Other cohomological bounds are discussed.

In many aspects the most complicated foliated manifolds are those with nonvanishing Godbillon-Vey class. We argue that they probably do not appear in physics and that is due to gauge symmetry which prevents the foliation from becoming “too wild”; that means that the foliation does not develop resilient leaves which, at least in codim-1, by Duminy’s theorem are responsible for the appearence of ...

Anti-de Sitter (AdS) space can be foliated by a family of nested surfaces homeomorphic to the boundary of the space. We propose a holographic correspondence between theories living on each surface in the foliation and quantum gravity in the enclosed volume. The flow of observables between our “interior” theories is described by a renormalization group equation. The dependence of these flows on ...

We give examples of foliations on suspensions and comment on their topological and geometric properties 1. Idea of foliation by suspension Here is the simplest example of foliation by suspension. Let X be a manifold of dimension q, and let f : X → X be a bijection. Then we define the suspension M = S ×f X as the quotient of [0, 1]×X by the equivalence relation (1, x) ∼ (0, f (x)). M = S ×f X = ...

In this paper we discuss some structure problems regarding the foliation of Levi flat manifolds, i.e. those CR manifolds which are foliated by complex leaves or, equivalently, whose Levi form vanishes. Levi flat manifolds have a particular significance among CR manifolds, since due to their degenerate nature they often behave as “limit case”, or they are an obstruction in extension problems of ...

A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the 1-parameter family of hypersurfaces orthogonal to the curves, each of which inherits a metric and connection from the original manifold via orthogonal projections; this is th...

The popular Hamilton-Jacobi method first proposed by Brown and York for defining quasilocal quantities such as energy for spatially bound regions assumes that the timelike boundary is orthogonal to the foliation of the spacetime. Such a restriction is undesirable for both theoretical and computational reasons. We remove the orthog-onality assumption and show that it is more natural to focus on ...