Branching in the Universal Cover of Taut Foliations
نویسندگان
چکیده
We study the topology of codimension one taut foliations of closed orientable 3-manifolds which are smooth along the leaves. In particular, we focus on the lifts of these foliations to the universal cover, specifically when any set of leaves corresponding to nonseparable points in the leaf space can be totally ordered. We use the structure of branching in the lifted foliation to find conditions that ensure two nonseparable leaves are left invariant under the same covering translation. We also determine when the set of leaves nonseparable from a given leaf is finite up to the action of covering translations. The hypotheses for the results are satisfied by all Anosov foliations.
منابع مشابه
Three-manifolds, Foliations and Circles, I Preliminary Version
A manifold M slithers around a manifold N when the universal cover of M fibers over N so that deck transformations are bundle automorphisms. Three-manifolds that slither around S are like a hybrid between three-manifolds that fiber over S and certain kinds of Seifert-fibered three-manifolds. There are examples of non-Haken hyperbolic manifolds that slither around S. It seems conceivable that ev...
متن کاملTautly foliated 3-manifolds with no R-covered foliations
We provide a family of examples of graph manifolds which admit taut foliations, but no R-covered foliations. We also show that, with very few exceptions, R-covered foliations are taut.
متن کاملContact Structures on Elliptic
We show that an oriented elliptic 3-manifold admits a universally tight positive contact structure iff the corresponding group of deck transformations on S preserves a standard contact structure pointwise. We also relate universally tight contact structures on 3-manifolds covered by S to the exceptional isomorphism SO(4) = (SU(2) × SU(2))/±1. The main tool used is equivariant framings of 3-mani...
متن کاملGraph Manifolds Z-homology 3-spheres and Taut Foliations
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.
متن کاملA Higher Dimensional Generalization of Taut Foliations
A higher dimensional generalization of taut foliations is introduced. Tools from symplectic geometry are used to describe surgery constructions, and to study the space of leaves of this class of foliations. Codimension one foliations are too large a class of structures to obtain strong structure theorems for them. According to a theorem of Thurston [39] a closed manifold admits a codimension on...
متن کامل