Related papers: Contact resolutions of singular Jacobi structures

We discuss the integrability of Jacobi manifolds by contact groupoids, and then look at what the Jacobi point of view brings new into Poisson geometry. In particular, using contact groupoids, we prove a Kostant-type theorem on the…

We investigate potential spaces associated with Jacobi expansions. We prove structural and Sobolev-type embedding theorems for these spaces. We also establish their characterizations in terms of suitably defined fractional square functions.…

We describe combinatorial aspects of classical resolution of singularities that are free of characteristic and can be applied to singular foliations and vector fields as well as to functions and varieties. In particular, we give a…

In this paper we introduce a graded bracket of forms on multicontact manifolds. This bracket satisfies a graded Jacobi identity as well as two different versions of the Leibniz rule, one of them being a weak Leibniz rule, extending the…

Generalised contact structures are studied from the point of view of reduced generalised complex structures, naturally incorporating non-coorientable structures as non-trivial fibering. The infinitesimal symmetries are described in detail,…

We study constructions of contact forms on closed manifolds. A notion of strong symplectic fold structure is defined and we prove that there is a contact form on $M \x X$ provided that $M$ admits such a structure and $X$ is contact. This…

We introduce a variant of contact homology for convex open contact manifolds. As an application, we prove the existence of (in fact, infinitely many) exotic tight contact structures on $\mathbb{R}^{2n-1}$ for all $n>2$.

We study in this paper the remnants of the contact partial order on the orbits of the adjoint action of contactomorphism groups on their Lie algebras. Our main interest is a class of non-compact contact manifolds, called convex at infinity.

Toric orbifolds are a generalization of simplicial projective toric varieties. In this paper, we show that there is a resolution of singularities of a toric orbifold. In a different category, the class of quasi-contact toric manifolds…

In this paper we introduce the notion of infinite dimensional Jacobi structure to describe the geometrical structure of a class of nonlocal Hamiltonian systems which appear naturally when applying reciprocal transformations to Hamiltonian…

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.…

Nous montrons que les seules vari\'et\'es toriques munies d'une structure de contact sont, \`a isomorphisme pr\`es, les espaces projectifs complexes et les vari\'et\'es $\mathbb{P}_{\mathbb{P}^{1}\times\cdots\times\mathbb{P}^{1}}…

The Jacobi polynomial has been advocated by many authors as a useful tool to evolve non-singlet structure functions to higher $Q^2$. In this work, it is found that the convergence of the polynomial sum is not absolute, as there is always a…

We prove that every homotopy class of almost contact structures on a closed 5-dimensional manifold admits a contact structure.

It is demonstrated that the knowledge of a single and arbitrary solution of the three-dimension\-al Jacobi equations allows determining infinite families of new solutions, which are generally and explicitly constructed in what follows.…

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

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…

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…

Jacobi sigma models are two-dimensional topological non-linear field theories which are associated with Jacobi structures. The latter can be considered as a generalization of Poisson structures. After reviewing the main properties and…

We study contact structures on smooth complex projective varieties with a simple normal crossing divisor, generalizing some well-known results concerning the non-logarithmic case. In particular, we describe the structure of elementary log…