Related papers: Contact Singularities

Definition of generalized normal form for a system of ODEs corresponding to an infinitesimal symplectic or contact transformation near a singular point, with an arbitrary polynomial unperturbed part, and a method of its finding are…

We analyze the singularities of the two-point function in a conformal field theory at finite temperature. In a free theory, the only singularity is along the boundary light cone. In the holographic limit, a new class of singularities…

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.…

The existence of several exotic phenomena, such as duality and spectral anholonomy is pointed out in one-dimensional quantum wire with a single defect. The topological structure in the spectral space which is behind these phenomena is…

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.…

Let $D$ be a closed unit $2$-disk on the plane centered at the origin $O$, and $F$ be a smooth vector field such that $O$ is a unique singular point of $F$ and all other orbits of $F$ are simple closed curves wrapping once around $O$. Thus…

Let V be a real hypersurface of class C^k, k>=3, in a complex manifold M of complex dimension n+1, HT(V) the holomorphic tangent bundle to V giving the induced CR structure on V. Let \theta be a contact form for (V,HT(V)), \xi_0 the Reeb…

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…

In this paper we classify the unimodal isolated complete intersection singularities in arbitrary characteristic under contact equivalence. The classification over $\mathbb{C}$ has already done by A. Dimca and C.G. Gibson. We continue and…

We collect some classical results about holomorphic 1-forms of a reduced complex curve singularity. They are used to study the pull-back of holomorphic 1-forms on an isolated complete intersection curve singularity under the normalization…

We consider the sphere $\Sph^{2n+1}$ equipped with its standard CR structure. In this paper we construct explicit contact forms on $\Sph^{2n+1}\setminus \Sph^{2k+1}$, which are conformal to the standard one and whose related Webster metrics…

The short-distance singularity of the product of a composite scalar field that deforms a field theory and an arbitrary composite field can be expressed geometrically by the beta functions, anomalous dimensions, and a connection on the…

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 generalize a theorem of Delzant classifying compact connected symplectic manifolds with completely integrable torus actions to certain singular symplectic spaces. The assumption on singularities is that if they are not finite quotient…

Given a complex analytic singularity $(X, 0)$, we show that if there exists an automorphism $F: (X, 0) \to (X, 0)$ that is contracting, then $(X, 0)$ is quasi-homogeneous.

For a graph $G=(V,E)$, and a symplectic vector space $(W, \left<\cdot,\cdot\right>)$, we define a variety $X(G,W)$ consisting of all functions $w:V\to W$ satisfying $\left<w(u), w(v)\right> = 0$ for any edge $\{u,v\}$ in $G$. We study the…

Using standard methods for studying singularities of projections and of contacts, we classify the stable singularities of affine $\lambda$-equidistants of $n$-dimensional closed submanifolds of $\mathbb R^q$, for $q\leq 2n$, whenever…

We describe some natural relations connecting contact geometry, classical Monge-Ampere equations and theory of singularities of solutions to nonlinear PDEs. They reveal the hidden meaning of Monge-Ampere equations and sheds new light on…

We study generalized almost contact structures on odd-dimensional manifolds. We introduce a notion of integrability and show that the class of these structures is closed under symmetries of the Courant-Dorfman bracket, including T-duality.…

This paper helps to clarify the status of cylindrical contact homology, a conjectured contact invariant introduced by Eliashberg, Givental, and Hofer in 2000. We explain how heuristic arguments fail to yield a well-defined homological…