Related papers: Orderable Contact Structures on Liouville-fillable…

We construct open book structures on all moment-angle manifolds and describe the topology of their leaves and bindings under certain restrictions. II. We also show, using a recent deep result about contact forms due to Borman, Eliashberg…

We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of…

We show that certain classes of contact 3-manifolds do not admit non-separating contact type embeddings into any closed symplectic 4-manifolds, e.g. this is the case for all contact manifolds that are (partially) planar or have Giroux…

We study smooth proper embeddings of compact orientable surfaces in compact orientable $4$-manifolds and elements in the mapping class group of that surface which are induced by diffeomorphisms of the ambient $4$-manifolds. We call such…

We prove that, under some natural conditions, Hamiltonian systems on a contact manifold $C$ can be split into a Reeb dynamics on an open subset of $C$ and a Liouville dynamics on a submanifold of $C$ of codimension 1. For the Reeb dynamics…

We study fillings of contact structures supported by planar open books by analyzing positive factorizations of their monodromy. Our method is based on Wendl's theorem on symplectic fillings of planar open books. We prove that every…

We adapt the Ozsv\'ath-Szab\'o full path algorithm to every star-shaped graph and establish a correspondence between negative-twisting tight contact structures on any Seifert fibred space over $S^2$, and its Heegaard Floer homology groups…

We characterize the oriented Seifert-fibered three-manifolds which admit positive, transverse contact structures.

We calculate the sutured version of cylindrical contact homology of a sutured contact solid torus $(S^1\times D^2,\Gamma, \xi)$, where $\Gamma$ consists of $2n$ parallel sutures of arbitrary slope and $\xi$ is a universally tight contact…

Let $V$ be a closed 3-manifold with a contact form $\lambda$, and let $L$ be a link consisting of closed orbits for the Reeb vector field of $\lambda$. We study the problem of defining cylindrical contact homology on the non-compact…

This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact…

In this paper we study the uniqueness of Lagrangian fillings of the standard Legendrian sphere $\mathcal{L}_0$ in the standard contact sphere $(S^{2n-1}, \xi_{\text st})$. We show that every exact Maslov zero Lagrangian filling $L$ of…

We exhibit the first examples of contact structures on $S^{2n-1}$ with $n\geq 4$ and on $S^3\times S^2$, all equipped with their standard smooth structures, for which every Reeb flow has positive topological entropy. As a new technical tool…

We study Legendrian embeddings of a compact Legendrian submanifold $L$ sitting in a closed contact manifold $(M,\xi)$ whose contact structure is supported by a (contact) open book $\mathcal{OB}$ on $M$. We prove that if $\mathcal{OB}$ has…

We show that the canonical contact structure on the link of a normal complex singularity is universally tight. As a corollary we show the existence of closed, oriented, atoroidal 3-manifolds with infinite fundamental groups which carry…

A two-dimensional open book (S,h) determines a closed, oriented three-manifold Y(S,h) and a contact structure C(S,h) on Y(S,h). The contact structure C(S,h) is Stein fillable if h is positive, i.e. h can be written as a product of…

We prove a contact non-squeezing result for a class of embeddings between starshaped domains in the contactization of the symplectization of the unit cotangent bundle of certain manifolds. The class of embeddings includes embeddings which…

In this paper, we determine the Euler characteristics and signatures of the exact symplectic fillings of the contact double, 3-fold or 4-fold cyclic covers of the standard contact 3-sphere branched over certain transverse quasi-positive…

Let M be a smooth compact connected manifold, on which there exists an effective smooth circle action preserving a positive smooth volume. We show that on M, the smooth closure of the smooth volume-preserving conjugation class of some…

In this note we will determine which contact structures on manifolds obtained by certain surgeries on the right handed trefoil are Stein fillable and which are not. This continues a long line of research and shows that there seems to be few…