Corpus ID: 235765561

Pseudoholomoprhic curves on the $\mathfrak{LCS}$-fication of contact manifolds

@inproceedings{Oh2021PseudoholomoprhicCO,
  title={Pseudoholomoprhic curves on the \$\mathfrak\{LCS\}\$-fication of contact manifolds},
  author={Y. G. Oh and Yasha Savelyev},
  year={2021}
}
For each contact diffeomorphism φ : (Q, ξ) → (Q, ξ) of (Q, ξ), we equip its mapping torus Mφ with a locally conformal symplectic form of Banyaga’s type, which we call the lcs mapping torus of contact diffeomorphism φ. In the present paper, we consider the product Q× S = Mid (corresponding to φ = id) and develop basic analysis of the associated J-holomorphic curve equation, which has the form ∂ π w = 0, wλ ◦ j = fdθ for the map u = (w, f) : Σ̇ → Q× S for the λ-compatible almost complex structure… Expand

References

SHOWING 1-10 OF 28 REFERENCES
Examples of non dω-exact locally conformal symplectic forms
Abstract.We exhibit two three-parameter families of locally conformal symplectic forms on the solvmanifold Mn,k considered in [1], and show, using the Hodge-de Rham theory for the LichnerowiczExpand
Deformations of coisotropic submanifolds in locally conformal symplectic manifolds
In this paper, we study deformations of coisotropic submanifolds in a locally conformal symplectic manifold. Firstly, we derive the equation that governs $C^\infty$ deformations of coisotropicExpand
Geometry of contact transformations and domains: orderability versus squeezing
Gromov’s famous non-squeezing theorem (1985) states that the standard symplectic ball cannot be symplectically squeezed into any cylinder of smaller radius. Does there exist an analogue of thisExpand
Analysis of Contact Cauchy-Riemann maps I: a priori $C^k$ estimates and asymptotic convergence
In the present article, we develop the analysis of the following nonlinear elliptic system of equations $$ \bar\partial^\pi w = 0, \, d(w^*\lambda \circ j) = 0 $$ first introduced by Hofer,Expand
ANALYSIS OF CONTACT CAUCHY–RIEMANN MAPS II: CANONICAL NEIGHBORHOODS AND EXPONENTIAL CONVERGENCE FOR THE MORSE–BOTT CASE
This is a sequel to the papers Oh and Wang (Real and Complex Submanifolds, Springer Proceedings in Mathematics and Statistics 106 (2014), 43–63, eds. by Y.-J. Suh and et al. for ICM-2014 satelliteExpand
Some properties of locally conformal symplectic structures
Abstract. We show that the $ d_{\omega} $-cohomology is isomorphic to a conformally invariant usual de Rham cohomology of an appropriate cover. We also prove a Moser theorem for locally conformalExpand
A Morse-Bott approach to contact homology
Contact homology was introduced by Eliashberg, Givental and Hofer; this contact invariant is based on J-holomorphic curves in the symplectization of a contact manifold. We expose an extension ofExpand
On nonseparating contact hypersurfaces in symplectic 4-manifolds
We show that certain classes of contact 3-manifolds do not admit nonseparating contact type embeddings into any closed symplectic 4-manifold, eg this is the case for all contact manifolds that areExpand
On the Group of Diffeomorphisms Preserving a Locally Conformal Symplectic Structure
The automorphism group of a locally conformal symplectic structure is studied. It is shown that this group possesses essential features of the symplectomorphism group. By using a special type ofExpand
Introduction to Symplectic Field Theory
We sketch in this article a new theory, which we call Symplectic Field Theory or SFT, which provides an approach to Gromov-Witten invariants of symplectic manifolds and their Lagrangian submanifoldsExpand
...
1
2
3
...