Related papers: Structures de contact sur les vari\'et\'es torique…
Nous consid\'erons un espace topologique qui est localement isomorphe au quotient de R^k par l'action d'un groupe discret et nous l'appelons quasi-vari\'et\'e de dimension k. Les quasi-vari\'et\'es g\'en\'eralisent les vari\'et\'es et les…
The complex projective structures considered is this article are compact curves locally modeled on $\mathbb{CP}^1$. To such a geometric object, modulo marked isomorphism, the monodromy map associates an algebraic one: a representation of…
We prove the existence of lattice isomorphic line arrangements having $\pi_1$-equivalent or homotopy-equivalent complements and non homeomorphic embeddings in the complex projective plane. We also provide two explicit examples, one is…
In this paper we generalize the main notions from the geometry of (almost) contact manifolds in the category of Lie algebroids. Also, using the framework of generalized geometry, we obtain an (almost) contact Riemannian Lie algebroid…
We give examples of contactomorphisms in every dimension that are smoothly isotopic to the identity but that are not contact isotopic to the identity. In fact, we prove the stronger statement that they are not even symplectically…
This paper explicitly describes Hodge structures of complete intersections of ample hypersurfaces in compact simplicial toric varieties.
We study left invariant contact forms and left invariant symplectic forms on Lie groups. We give the classification of all symplectic structures on nilpotent Lie algebras up the dimension 6.
In this paper we show that any good toric contact manifold has well defined cylindrical contact homology and describe how it can be combinatorially computed from the associated moment cone. As an application we compute the cylindrical…
If $\eta$ is a contact form on a manifold $M$ such that the orbits of the Reeb vector field form a simple foliation $\mathcal{F}$ on $M$, then the presymplectic 2-form $d\eta$ on $M$ induces a symplectic structure $\omega$ on the quotient…
We introduce a notion of positive pair of contact structures on a 3-manifold which generalizes a previous definition of Eliashberg-Thurston and Mitsumatsu. Such a pair gives rise to a locally integrable plane field $\lambda$. We prove that…
A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, which is called a real structure. A real contact 3-manifold is a real 3-manifold with a contact distribution that is antisymmetric with…
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,…
Let $X$ be a rationally connected smooth projective variety of dimension $n$. We show that $X$ is a toric variety if and only if $X$ admits an int-amplified endomorphism with totally invariant ramification divisor. We also show that $X\cong…
A general problem in complex cobordism theory is to find useful representatives for cobordism classes. One particularly convenient class of complex manifolds consists of smooth projective toric varieties. The bijective correspondence…
In this note we study contact structures on 5-dimensional manifolds. We give a complete answer under the assumption that the Abundance conjecture holds in dimension 5.
In this article, we find the complete list of all contact structures (up to isotopy) on closed three-manifolds which are supported by an open book decomposition having planar pages with three (but not less) boundary components. We…
Limited bonding valence, usually accompanied by well-defined directional interactions and selective bonding mechanisms, is nowadays considered among the key ingredients to create complex structures with tailored properties: even though…
We consider tight contact structures on plumbed 3-manifolds with no bad vertices. We discuss how one can count the number of tight contact structures with zero Giroux torsion on such 3-manifolds and explore conditions under which Giroux…
Two constructions of contact manifolds are presented: (i) products of S^1 with manifolds admitting a suitable decomposition into two exact symplectic pieces and (ii) fibre connected sums along isotropic circles. Baykur has found a…
In this paper, we focus on contact structures supported by planar open book decompositions. We study right-veering diffeomorphisms to keep track of overtwistedness property of contact structures under some monodromy changes. As an…