Related papers: Contact non-squeezing and orderability via the sha…

The first two authors showed in~\cite{AM1} how the Conley-Zehnder index of any contractible periodic Reeb orbit of a non-degenerate toric contact form on a good toric contact manifold with zero first Chern class, i.e. a Gorenstein toric…

We compute the homotopy type of the space of embeddings of convex disks with Legendrian boundary into a tight contact $3$-manifold, whenever the sum of the absolute value of the rotation number of the boundary with the Thurston-Bennequin…

Given a contact structure on a manifold $V$ together with a supporting open book decomposition, Bourgeois gave an explicit construction of a contact structure on $V \times \mathbb{T}^2$. We prove that all such structures are universally…

Codimension 2 contact submanifolds are the natural generalization of transverse knots to contact manifolds of arbitrary dimension. In this paper, we construct new invariants of codimension 2 contact submanifolds. Our main invariant can be…

By a result of Eliashberg, every symplectic filling of a three-dimensional contact connected sum is obtained by performing a boundary connected sum on another symplectic filling. We prove a partial generalization of this result for…

This paper is an overview of the idea of using contact geometry to construct invariants of immersions and embeddings. In particular, it discusses how to associate a contact manifold to any manifold and a Legendrian submanifold to an…

This paper helps to clarify the status of cylindrical contact homology, a conjectured contact invariant introduced by Eliashberg, Givental, and Hofer in 2000. We explain how heuristic arguments fail to yield a well-defined homological…

We prove that isomorphism classes of principal bundles over a diffeological space are in bijection to certain maps on its free loop space, both in a setup with and without connections on the bundles. The maps on the loop space are smooth…

We prove that every non-degenerate Reeb flow on a closed contact manifold $M$ admitting a strong symplectic filling $W$ with vanishing first Chern class carries at least two geometrically distinct closed orbits provided that the positive…

In this paper, we study contact structures on any open 3-manifold V which is the interior of a compact 3-manifold. To do this, we introduce proper contact isotopy invariants called the slope at infinity and the division number at infinity.…

A new characterization is provided for the class of compact rank-one symmetric spaces. Such spaces are the only symmetric spaces of compact type for which the standard vector field on their sphere bundles is Killing with respect to some…

We show that for a large class of contact 3-manifolds the groups of Vassiliev invariants of Legendrian and of framed knots are canonically isomorphic. As a corollary, we obtain that the group of finite order Arnold's $J^+$-type invariants…

We extend the theorems concerning the equivariant symplectic reduction of the cotangent bundle to contact geometry. The role of the cotangent bundle is taken by the cosphere bundle. We use Albert's method for reduction at zero and Willett's…

We consider an entropy-type invariant which measures the polynomial volume growth of submanifolds under the iterates of a map, and we establish sharp uniform lower bounds of this invariant for the following classes of symplectomorphisms of…

We formulate the non-commutative integrability of contact systems on a contact manifold $(M,\mathcal H)$ using the Jacobi structure on the space of sections $\Gamma(L)$ of a contact line bundle $L$. In the cooriented case, if the line…

We define \emph{$0$-shifted} and \emph{$+1$-shifted contact structures} on differentiable stacks, thus laying the foundations of \emph{shifted Contact Geometry}. As a side result we show that the kernel of a multiplicative $1$-form on a Lie…

This article clarifies the status of linearized contact homology given the foundations of the contact dg-algebra established by Pardon. In particular, we prove that the set of isomorphism classes of linearized contact homologies of a closed…

We construct infinitely many non-diffeomorphic examples of $5$-dimensional contact manifolds which are tight, admit no strong fillings, and do not have Giroux torsion. We obtain obstruction results for symplectic cobordisms, for which we…

We introduce a pseudo-metric on the contactomorphism group of any contact manifold $(M,\xi)$ with a cooriented contact structure $\xi$. It is the contact analogue of a corresponding semi-norm in Hofer's geometry, and on certain classes of…

Let S^3_r(K) be the oriented 3--manifold obtained by rational r-surgery on a knot K in S^3. Using the contact Ozsvath-Szabo invariants we prove, for a class of knots K containing all the algebraic knots, that S^3_r(K) carries positive,…