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  • Concentration of symplectic volumes on Poisson homogeneous spaces
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-09-01
    Anton Alekseev; Benjamin Hoffman; Jeremy Lane; Yanpeng Li

    For a compact Poisson–Lie group $K$, the homogeneous space $K/T$ carries a family of symplectic forms $\omega^s_\xi$, where $\xi \in \mathfrak{t}^{\ast}_{+}$ is in the positive Weyl chamber and $s \in \mathbb{R}$. The symplectic form $\omega^0_\xi$ is identified with the natural $K$-invariant symplectic form on the $K$ coadjoint orbit corresponding to $\xi$. The cohomology class of $\omega^s_\xi$ is

    更新日期:2020-10-30
  • $J$-holomorphic cylinders between ellipsoids in dimension four
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-09-01
    Richard K. Hind; Ely Kerman

    We establish the existence of regular $J$‑holomorphic cylinders in $4$‑dimensional ellipsoid cobordisms that are asymptotic to Reeb orbits of small Conley–Zehnder index. We also give an independent proof of the existence of cylindrical holomorphic buildings in $4$‑dimensional ellipsoid cobordisms under fairly general conditions.

    更新日期:2020-10-30
  • Elliptic diffeomorphisms of symplectic $4$-manifolds
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-09-01
    Vsevolod Shevchishin; Gleb Smirnov

    We show that symplectically embedded $(-1)$‑tori give rise to certain elements in the symplectic mapping class group of $4$‑manifolds. An example is given where such elements are proved to be of infinite order.

    更新日期:2020-10-30
  • Symplectically replacing plumbings with Euler characteristic $2 \: 4$‑manifolds
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-09-01
    Jonathan Simone

    We introduce new symplectic cut-and-paste operations that generalize the rational blowdown. In particular, we will define $k$‑replaceable plumbings to be those that, heuristically, can be symplectically replaced by Euler characteristic $k \: 4$‑manifolds. We will then classify $2$‑replaceable linear plumbings, construct $2$‑replaceable plumbing trees, and use one such tree to construct a symplectic

    更新日期:2020-10-30
  • Almost-Kähler smoothings of compact complex surfaces with $A_1$ singularities
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-09-01
    Caroline Vernier

    This paper is concerned with the existence of metrics of constant Hermitian scalar curvature on almost-Kähler manifolds obtained as smoothings of a constant scalar curvature Kähler orbifold, with $A_1$ singularities. More precisely, given such an orbifold that does not admit nontrivial holomorphic vector fields, we show that an almost-Kähler smoothing $(M_\varepsilon , \omega_\varepsilon)$ admits an

    更新日期:2020-10-30
  • Symplectic toric stratified spaces with isolated singularities
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-09-01
    Seth Wolbert

    The goal of this paper is to classify symplectic toric stratified spaces with isolated singularities. This extends a result of Burns, Guillemin, and Lerman which carries out this classification in the compact connected case. In making this classification, it is necessary to classify symplectic toric cones. Via a well-known equivalence between symplectic toric cones and contact toric manifolds, this

    更新日期:2020-10-30
  • Persistence-like distance on Tamarkin’s category and symplectic displacement energy
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-05-01
    Tomohiro Asano; Yuichi Ike

    We introduce a persistence-like pseudo-distance on Tamarkin’s category and prove that the distance between an object and its Hamiltonian deformation is at most the Hofer norm of the Hamiltonian function. Using the distance, we show a quantitative version of Tamarkin’s non-displaceability theorem, which gives a lower bound of the displacement energy of compact subsets of cotangent bundles.

    更新日期:2020-05-01
  • Loose Legendrian and pseudo-Legendrian knots in $3$-manifolds
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-05-01
    Patricia Cahn; Vladimir Chernov

    We prove a complete classification theorem for loose Legendrian knots in an oriented $3$-manifold, generalizing results of Dymara and Ding-Geiges. Our approach is to classify knots in a $3$-manifold $M$ that are transverse to a nowhere-zero vector field $V$ up to the corresponding isotopy relation. Such knots are called $V$-transverse. A framed isotopy class is simple if any two $V$-transverse knots

    更新日期:2020-05-01
  • Positive topological entropy of positive contactomorphisms
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-05-01
    Lucas Dahinden

    A positive contactomorphism of a contact manifold $M$ is the end point of a contact isotopy on $M$ that is always positively transverse to the contact structure. Assume that $M$ contains a Legendrian sphere $\Lambda$, and that $(M, \Lambda)$ is fillable by a Liouville domain $(W, \omega)$ with exact Lagrangian $L$. We show that if the exponential growth of the action filtered wrapped Floer homology

    更新日期:2020-05-01
  • H-principle for complex contact structures on Stein manifolds
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-05-01
    Franc Forstnerič

    In this paper we introduce the notion of a formal complex contact structure on an odd dimensional complex manifold. Our main result is that every formal complex contact structure on a Stein manifold, $X$, is homotopic to a holomorphic contact structure on a Stein domain $\Omega \subset X$ which is diffeotopic to $X$. We also prove a parametric h‑principle in this setting, analogous to Gromov’s h‑principle

    更新日期:2020-05-01
  • Ideal Liouville Domains, a cool gadget
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-05-01
    Emmanuel Giroux

    Liouvile domains are central objects in symplectic geometry today, but they have unsatisfactory aspects due to the requested choice of Liouville forms and to the non-compactness of their completions. Ideal Liouville domains, in contrast, are compact manifolds with boundary merely equipped with a symplectic form in the interior. Still, their isomorphism classes are in one-to-one correspondence with

    更新日期:2020-05-01
  • Symplectic and Kähler structures on biquotients
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-05-01
    Oliver Goertsches; Panagiotis Konstantis; Leopold Zoller

    We construct symplectic structures on roughly half of all equal rank biquotients of the form $G //T$, where $G$ is a compact simple Lie group and $T$ a torus, and investigate Hamiltonian Lie group actions on them. For the Eschenburg flag, this action has similar properties as Tolman’s and Woodward’s examples of Hamiltonian non-Kähler actions. In addition to the previously known Kähler structure on

    更新日期:2020-05-01
  • The fundamental groups of contact toric manifolds
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-05-01
    Hui Li

    Let $M$ be a connected compact contact toric manifold. Most of such manifolds are of Reeb type. We show that if $M$ is of Reeb type, then $\pi_1 (M)$ is finite cyclic, and we describe how to obtain the order of $\pi_1 (M)$ from the moment map image.

    更新日期:2020-05-01
  • Coisotropic Hofer–Zehnder capacities and non-squeezing for relative embeddings
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-05-01
    Samuel Lisi; Antonio Rieser

    We introduce the notion of a symplectic capacity relative to a coisotropic submanifold of a symplectic manifold, and we construct two examples of such capacities through modifications of the Hofer–Zehnder capacity. As a consequence, we obtain a non-squeezing theorem for symplectic embeddings relative to coisotropic constraints and existence results for leafwise chords on energy surfaces.

    更新日期:2020-05-01
  • Positive loops of loose Legendrian embeddings and applications
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-05-01
    Guogang Liu

    In this paper, we prove that there exist contractible positive loops of Legendrian embeddings based at any loose Legendrian submanifold. As an application, we define a partial order on $\widetilde{Cont}_0 (M, \xi)$, called strong orderability, and prove that overtwisted contact manifolds are not strongly orderable.

    更新日期:2020-05-01
  • Spinor modules for Hamiltonian loop group spaces
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-05-01
    Yiannis Loizides; Eckhard Meinrenken; Yanli Song

    Let $LG$ be the loop group of a compact, connected Lie group $G$. We show that the tangent bundle of any proper Hamiltonian $LG$-space $\mathcal{M}$ has a natural completion $\overline{T}\mathcal{M}$ to a strongly symplectic $LG$-equivariant vector bundle. This bundle admits an invariant compatible complex structure within a natural polarization class, defining an $LG$-equivariant spinor bundle $\

    更新日期:2020-05-01
  • A new approach to the symplectic isotopy problem
    J. Symplectic Geom. (IF 0.657) Pub Date : 2020-05-01
    Laura Starkston

    The symplectic isotopy conjecture states that every smooth symplectic surface in $\mathbb{C}\mathrm{P}^2$ is symplectically isotopic to a complex algebraic curve. Progress began with Gromov’s pseudoholomorphic curves [Gro85], and progressed further culminating in Siebert and Tian’s proof of the conjecture up to degree $17$ [ST05], but further progress has stalled. In this article we provide a new direction

    更新日期:2020-05-01
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