Related papers: Contact resolutions of singular Jacobi structures

In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.

We survey what is known about various special types of submanifolds of contact manifolds and discuss their role in the development of contact geometry.

We study precontact groupoids whose infinitesimal counterparts are Dirac-Jacobi structures. These geometric objects generalize contact groupoids. We also explain the relationship between precontact groupoids and homogeneous presymplectic…

The projectivised nilpotent orbit closure P(\bar{O}) carries a natural contact structure on its smooth part. A resolution X \to P(\bar{O}) is called contact if the contact structure on P(O) extends to a contact structure on X. It turns out…

We consider a local algebra A (in the sense of Andr\'e Weil), M a smooth paracompact manifold and M^{A} the manifold of infinietly near points on M of kind A. In this paper, we define and study the notions of A-Jacobi structures on M^{A}.

We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e.,…

We describe totally compatible structures on the Jacobson radical of the incidence algebra of a finite poset over a field. We show that such structures are in general non-proper.

Using the adjoint representations of Lie algebras, we classify all Jacobi structures on real two- and three-dimensional Lie groups. Also, we study Jacobi-Lie systems on these real low-dimensional Lie groups. Our results are illustrated…

This is the second part of a series of two papers dedicated to a systematic study of holomorphic Jacobi structures. In the first part, we introduced and study the concept of a holomorphic Jacobi manifold in a very natural way as well as…

We describe a contact analog of the symplectic cut construction. As an application we show that the group of contactomorphisms for a particular overtwisted contact structure on the three sphere contains countably many nonconjugate two tori.

The formulation of covariant brackets on the space of solutions to a variational problem is analyzed in the framework of contact geometry. It is argued that the Poisson algebra on the space of functionals on fields should be read as a…

We study some properties of transverse contact structures on small Seifert manifolds, and we apply them to the classification of tight contact structures on a family of small Seifert manifolds.

In this article we introduce and analyze in detail singular contact structures, with an emphasis on $b^m$-contact structures, which are tangent to a given smooth hypersurface $Z$ and satisfy certain transversality conditions. These singular…

In this paper, we construct complex metric structures on complex hypersurfaces in hyperkahler manifolds. This construction is that in contact geometry.

We develop a systematic approach to contact and Jacobi structures on graded supermanifolds. In this framework, contact structures are interpreted as symplectic principal GL(1,R)-bundles. Gradings compatible with the GL(1,R)-action lead to…

In discrete geometry, the contact number of a given finite number of non-overlapping spheres was introduced as a generalization of Newton's kissing number. This notion has not only led to interesting mathematics, but has also found…

We study Jacobi matrices on trees with one end at inifinity. We show that the defect indices cannot be greater than 1 and give criteria for essential selfadjointness. We construct certain polynomials associated with matrices, which mimic…

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.

The geometric properties of sigma models with target space a Jacobi manifold are investigated. In their basic formulation, these are topological field theories - recently introduced by the authors - which share and generalise relevant…

We construct (infinitely many) examples in all dimensions of contactomorphisms of closed overtwisted contact manifolds that are smoothly isotopic but not contact-isotopic to the identity.