REVIEW 3 cited by
Intersection of transverse foliations in 3-manifolds: Hausdorff leafspace implies leafwise quasi-geodesic
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
Let $\mathcal{F}_1$ and $\mathcal{F}_2$ be transverse two dimensional foliations with Gromov hyperbolic leaves in a closed 3-manifold $M$ whose fundamental group is not solvable, and let $\mathcal{G}$ be the one dimensional foliation obtained by intersection. We show that $\mathcal{G}$ is \emph{leafwise quasigeodesic} in $\mathcal{F}_1$ and $\mathcal{F}_2$ if and only if the foliation $\mathcal{G}_L$ induced by $\mathcal{G}$ in the universal cover $L$ of any leaf of $\mathcal{F}_1$ or $\mathcal{F}_2$ has Hausdorff leaf space. We end up with a discussion on the hypothesis of Gromov hyperbolicity of the leaves.
Forward citations
Cited by 3 Pith papers
-
Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three
Conservative partially hyperbolic diffeomorphisms homotopic to the identity on closed 3-manifolds with non-virtually-solvable fundamental group are always accessible and hence ergodic.
-
Partially Hyperbolic Dynamics with Quasi-isometric Center
Non-wandering partially hyperbolic diffeomorphisms with quasi-isometric center on closed 3-manifolds are either skew products over a torus Anosov map or discretized Anosov flows, and volume-preserving ones are ergodic.
-
Quasi-isometric center action in dimension 3
Transitive partially hyperbolic diffeomorphisms in dimension 3 that act quasi-isometrically on an invariant center foliation are classified up to finite lift and iterate as skew-products or discretised Anosov flows.
Discussion (0). Continue with ORCID to comment.