Related papers: Every real 3-manifold is real contact

A complex contact threefold is a threefold with a two-dimensional non-integrable holomorphic distribution. A contact curve on a contact threefold is an integrable curve of the distribution. This work was inspired by two papers of Bryant, in…

We consider compact 3-manifolds M having a submersion h to R in which each generic point inverse is a planar surface. The standard height function on a submanifold of the 3-sphere is a motivating example. To (M, h) we associate a…

We give necessary and sufficient conditions for a closed orientable 9-manifold M to admit an almost contact structure. The conditions are stated in terms of the Stiefel-Whitney classes of M and other more subtle homotopy invariants of M. By…

It is an important question whether it is possible to put a geometry on a given manifold or not. It is well known that any simply connected closed manifold admitting a real projective structure must be a sphere. Therefore, any simply…

We execute Avdek's algorithm to find many algebraically overtwisted and tight $3$-manifolds by contact $+1$ surgeries. In particular, we show that a contact $1/k$ surgery on the standard contact $3$-sphere along any positive torus knot with…

Let $M$ be a non-compact hyperbolic $3$-manifold with finite volume and totally geodesic boundary components. By subdividing mixed ideal polyhedral decompositions of $M$, under some certain topological conditions, we prove that $M$ has an…

We prove that there is a knot $K$ transverse to $\xi_{std}$, the tight contact structure of $S^3$, such that every contact 3-manifold $(M, \xi)$ can be obtained as a contact covering branched along $K$. By contact covering we mean a map…

We prove that contact homeomorphisms preserve characteristic foliations on surfaces in contact $3$-manifolds. More precisely, since the characteristic foliation is a singular $1$-dimensional foliation, we show that singular points are…

In this article we show that in any dimension there exist infinitely many pairs of formally contact isotopic isocontact embeddings into the standard contact sphere which are not contact isotopic. This is the first example of rigidity for…

For contact manifolds, it is well-known that the map which assigns to an infinitesimal contact transformation its contact Hamiltonian function is a linear isomorphism, and an explicit local formula for its inverse can be given. In contrast,…

We show that there exists a transverse link in the standard contact structures on the 3-sphere such that all contact 3-manifolds are contact branched covers over this transverse link.

We describe a necessary and sufficient condition for a principal circle bundle over an even-dimensional manifold to carry an invariant contact structure. As a corollary it is shown that all circle bundles over a given base manifold carry an…

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…

Using recent work on high dimensional Lutz twists and families of Weinstein structures we show that any almost contact structure on a 5-manifold is homotopic to a contact structure.

The Newman-Penrose-Perjes formalism is applied to smooth contact structures on riemannian 3-manifolds. In particular it is shown that a contact 3-manifold admits an adapted riemannian metric if and only if it admits a metric with a…

A random group contains many subgroups which are isomorphic to the fundamental group of a compact hyperbolic 3-manifold with totally geodesic boundary. These subgroups can be taken to be quasi-isometrically embedded. This is true both in…

We use monopole Floer homology to study the topology of the space of contact structures on a 3-manifold. Our main tool is a generalisation of the Kronheimer--Mrowka--Ozsv\'ath--Szab\'o contact invariant to an invariant for families of…

According to a theorem of Eliashberg and Thurston a $C^2$-foliation on a closed 3-manifold can be $C^0$-approximated by contact structures unless all leaves of the foliation are spheres. Examples on the 3-torus show that every neighbourhood…

We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic…

We present a new, completely three-dimensional proof of the fact, due to Gabai-Eliashberg-Thurston, that every closed, oriented, irreducible 3-manifold with nonzero second homology carries a universally tight contact structure.