Related papers: Tight contact structures without symplectic fillin…

We classify the real tight contact structures on solid tori up to equivariant contact isotopy and apply the results to the classification of real tight structures on $S^3$ and real lens spaces $L(p,\pm 1)$. We prove that there is a unique…

In this short note, we give examples of binding sums of contact 3-manifolds that do not preserve properties such as tightness or symplectic fillability. We also prove vanishing of the Heegaard Floer contact invariant for an infinite family…

We classify closed, simply connected $n$-manifolds of non-negative sectional curvature admitting an isometric torus action of maximal symmetry rank in dimensions $2\leq n\leq 6$. In dimensions $3k$, $k=1,2$ there is only one such manifold…

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 exact orbifold fillings of contact manifolds using Floer theories. Motivated by Chen-Ruan's orbifold Gromov-Witten invariants, we define symplectic cohomology of an exact orbifold filling as a group using classical techniques, i.e.…

In this article we classify up to isotopy tight contact structures on Seifert manifolds over the torus with one singular fibre.

We construct explicit left invariant quaternionic contact structures on Lie groups with zero and non-zero torsion, and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of quaternionic contact…

Twists of contact structures in dimension 3 and higher are studied in this paper from a viewpoint of contact round surgery. Three kinds of new modifications of contact structures which are higher-dimensional generalizations of the…

We construct the first example of a 5-dimensional simply connected compact manifold that admits a K-contact structure but does not admit a semi-regular Sasakian structure. For this, we need two ingredients: (a) to construct a suitable…

We compute the Ozsv\'ath--Szab\'o contact invariants for all tight contact structures on the manifolds -\Sigma(2,3,6n-1).

We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. We classify these structures by their intrinsic torsion and review the literature in terms of this scheme. Moreover, we determine necessary and…

We consider contact structures on simply-connected 5-manifolds which arise as circle bundles over simply-connected symplectic 4-manifolds and show that invariants from contact homology are related to the divisibility of the canonical class…

We study several aspects of fillings for links of general quotient singularities using Floer theory, including co-fillings, Weinstein fillings, strong fillings, exact fillings and exact orbifold fillings, focusing on non-existence of exact…

In this note we study solid tori in contact manifolds. Specifically, we study the width of a knot type and give criteria for when it is equal to the maximal Thurston-Bennequin invariant, and when it is larger. We also prove there are many…

We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact…

Let $M_p$ be a circle bundle with first Chern class $p[\omega]$ over a closed $4n$-dimensional integral symplectic manifold $(\overline{M}, \omega)$. Equivalently, $M_p$ is a closed contact $(4n+1)$-manifold whose Reeb orbits are all closed…

We use the equivalence between embedded contact homology and Seiberg-Witten Floer homology to obtain the following improvements on the Weinstein conjecture. Let Y be a closed oriented connected 3-manifold with a stable Hamiltonian…

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…

If a contact form on a (2n+1)-dimensional closed contact manifold admits closed Reeb orbits, then its systolic ration is defined to be the quotient of (n+1)th power of the shortest period of Reeb orbits by the contact volume. We prove that…

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…