Related papers: Orderable Contact Structures on Liouville-fillable…

We study Liouville fillable contact manifolds $(\Sigma,\xi)$ with non-zero Rabinowitz Floer homology and assign spectral numbers to paths of contactomorphisms. As a consequence we prove that $\widetilde{\mathrm{Cont}_0}(\Sigma,\xi)$ is…

In this paper we are interested in characterizing the standard contact sphere in terms of dynamically convex contact manifolds which admit a Liouville filling with vanishing symplectic homology. We first observe that if the filling is…

We show by a counter example that any Liouville filling of a ADC closed contact manifold does not have isomorphic integral cohomologies.

We introduce a new method to obstruct Liouville and weak fillability. Using this, we show that various rational homology 3-spheres admit strongly fillable contact structures without Liouville fillings, which extends the result of Ghiggini…

We show that for all $n \ge 3$, any $(2n+1)$-dimensional manifold that admits a tight contact structure, also admits a tight but non-fillable contact structure, in the same almost contact class. For $n=2$, we obtain the same result,…

Positive loops of Legendrian embeddings are examined from the point of view of Floer homology of Lagrangian cobordisms. This leads to new obstructions to the existence of a positive loop containing a given Legendrian, expressed in terms of…

A positive contactomorphism of a contact manifold $M$ is the end point of a contact isotopy on $M$ that is always positively transverse to the contact structure. Assume that $M$ contains a Legendrian sphere $\Lambda$, and that $(M,\Lambda)$…

In this note, we consider contractible loops of contactomorphisms that are positive over some non-empty closed subset of a contact manifold. Such closed subsets are called immaterial. We argue that the complement of a Reeb-invariant…

In this article we address the existence of positive loops of contactomorphisms in overtwisted contact 3-folds. We present a construction of such positive loops in the contact fibered connected sum of certain contact 3-folds along…

We consider symplectic cohomology twisted by sphere bundles, which can be viewed as an analogue of local systems. Using the associated Gysin exact sequence, we prove the uniqueness of part of the ring structure on cohomology of fillings for…

We prove an inequality between the $L^{\infty}$-norm of the contact Hamiltonian of a positive loop of contactomorphims and the minimal Reeb period. This implies that there are no small positive loops on hypertight or Liouville fillable…

We prove, in a geometric way, that the standard contact structure on the real projective space of dimension $2n-1$ is not Liouville fillable for $n \ge 3$ and odd. We also prove that, for all $n$, semipositive fillings of those contact…

We prove that every strong symplectic filling of a planar contact manifold admits a symplectic Lefschetz fibration over the disk, and every strong filling of the 3-torus similarly admits a Lefschetz fibration over the annulus. It follows…

We show that positive $S^1$-equivariant symplectic homology is a contact invariant for a subclass of contact manifolds which are boundaries of Liouville domains. In nice cases, when the set of Conley-Zehnder indices of all good periodic…

In this note, we prove that every closed connected oriented odd-dimensional manifold admits a map of non-zero degree (i.e., a domination) from a tight contact manifold of the same dimension. This provides an odd-dimensional counterpart of a…

For any asymptotically dynamically convex contact manifold $Y$, we show that $SH_*(W)=0$ is a property independent of the choice of topologically simple (i.e.\ $c_1(W)=0$ and $\pi_{1}(Y)\rightarrow \pi_1(W)$ is injective) Liouville filling…

We consider the standard Darboux space equipped with the radial symmetric contact form. We study co-orientation preserving contactomorphisms between relatively compact domains up to the boundary. We determine the contactomorphism classes…

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…

We prove that on overtwisted contact manifolds there can be no positive loops of contactomorphisms that are generated by a $C^0$-small Hamiltonian function.

We show that an oriented elliptic 3-manifold admits a universally tight positive contact structure iff the corresponding group of deck transformations on $S^3$ preserves a standard contact structure pointwise. We also relate univerally…