A note on Mitsumatsu's construction of a leafwise symplectic foliation

Reeb components of leafwise complex foliations and their symmetries III

The automorphisms group of the 3-dimensional Reeb component with complex leaves is computed in the case where the component is obtained by the Hopf construction and the holonomy of the boundary leaf is not tangent to the identity to the infinite order. Combined with a previous work, for 3-dimensional Reeb components obtained by the Hopf construction, we have an almost complete description of the groups of leafwise holomorphic smooth automorphisms.

Some tight contact foliations can be approximated by overtwisted ones

A contact foliation is a foliation endowed with a leafwise contact structure. In this remark we explain a turbulisation procedure that allows us to prove that tightness is not a homotopy invariant property for contact foliations.

The dimension of the leafwise reduced cohomology

Geometric conditions are given so that the leafwise reduced cohomology is of infinite dimension, specially for foliations with dense leaves on closed manifolds. The main new definition involved is the intersection number of subfoliations with "appropriate coefficients". The leafwise reduced cohomology is also described for homogeneous foliations with dense leaves on closed nilmanifolds.

3维流形中横截叶状结构的交：Hausdorff叶空间蕴含叶状拟测地线

Intersection of transverse foliations in 3-manifolds: Hausdorff leafspace implies leafwise quasi-geodesic

本文研究闭3维流形中两横截二维叶状结构相交所产生的一维叶状结构，证明其叶状拟测地性质等价于万有覆盖中诱导叶状结构具有 Hausdorff 叶空间。

Analysis on Riemannian foliations of bounded geometry

A leafwise Hodge decomposition was proved by Sanguiao for Riemannian foliations of bounded geometry. Its proof is explained again in terms of our study of bounded geometry for Riemannian foliations. It is used to associate smoothing operators to foliated flows, and describe their Schwartz kernels. All of this is extended to a leafwise version of the Novikov differential complex.

On closed leaves of foliations, multisections and stable commutator lengths

We give examples of foliations that answer two questions posed by Mitsumatsu and Vogt about the genus minimising properties of closed leaves of 2-dimensional foliations on 4-manifolds. By studying stable commutator lengths in certain stable mapping class groups, we also answer an asymptotic version of another question of theirs concerning bounds on self-intersection numbers of multisections in surface bundles.

Paires de structures de contact sur les variétés de dimension trois

We introduce a notion of positive pair of contact structures on a 3-manifold which generalizes a previous definition of Eliashberg-Thurston and Mitsumatsu. Such a pair gives rise to a locally integrable plane field $λ$. We prove that if $λ$ is uniquely integrable and if both structures of the pair are tight, then the integral foliation of $λ$ doesn't contain any Reeb component whose core curve is homologous to zero. Moreover, the ambient manifold carries a Reebless foliation. We also show a stability theorem "à la Reeb" for positive pairs of tight contact structures.

Conformal Symplectic structures, Foliations and Contact Structures

This paper presents two existence h-principles, the first for conformal symplectic structures on closed manifolds, and the second for leafwise conformal symplectic structures on foliated manifolds with non empty boundary. The latter h-principle allows to linearly deform certain codimension-$1$ foliations to contact structures. These results are essentially applications of the Borman-Eliashberg-Murphy h-principle for overtwisted contact structures and of the Eliashberg-Murphy symplectization of cobordisms, together with tools pertaining to foliated Morse theory, which are elaborated here.

Morse-Novikov cohomology on foliated manifolds

The idea of Lichnerowicz or Morse-Novikov cohomology groups of a manifold has been utilized by many researchers to study important properties and invariants of a manifold. Morse-Novikov cohomology is defined using the differential $d_ω=d+ω\wedge$, where $ω$ is a closed $1$-form. We study Morse-Novikov cohomology relative to a foliation on a manifold and its homotopy invariance and then extend it to more general type of forms on a Riemannian foliation. We study the Laplacian and Hodge decompositions for the corresponding differential operators on reduced leafwise Morse-Novikov complexes. In the…

Leafwise smoothing laminations

We show that every topological surface lamination of a 3-manifold M is isotopic to one with smoothly immersed leaves. This carries out a project proposed by Gabai in [Problems in foliations and laminations, AMS/IP Stud. Adv. Math. 2.2 1--33]. Consequently any such lamination admits the structure of a Riemann surface lamination, and therefore useful structure theorems of Candel [Uniformization of surface laminations, Ann. Sci. Ecole Norm. Sup. 26 (1993) 489--516] and Ghys [Dynamique et geometrie complexes, Panoramas et Syntheses 8 (1999)] apply.

Taut foliations and the actions of fundamental groups on leaf spaces and universal circles

Let $F$ be a leafwise hyperbolic taut foliation of a closed 3-manifold $M$ and let $L$ be the leaf space of the pullback of $F$ to the universal cover of $M$. We show that if $F$ has branching, then the natural action of $π_1(M)$ on $L$ is faithful. We also show that if $F$ has a finite branch locus $B$ whose stabilizer acts on $B$ nontrivially, then the stabilizer is an infinite cyclic group generated by an indivisible element of $π_1(M)$.

紧叶状结构和阿诺索夫流的刘维尔结构的拓扑不变性

Topological invariance of Liouville structures for taut foliations and Anosov flows

研究闭定向三维流形上紧叶状结构相关的刘维尔结构的拓扑不变性，通过特定方法证明其为拓扑不变量，还涉及阿诺索夫流弱叶状结构及轨道等价情况，证明结合平滑方案和沃格尔结果，附录用于构造新例子助于分类。