Essential tori in spaces of symplectic embeddings

  title={Essential tori in spaces of symplectic embeddings},
  author={Julian Chaidez and Mihail Munteanu},
  journal={Algebraic \& Geometric Topology},
Given two $2n$--dimensional symplectic ellipsoids whose symplectic sizes satisfy certain inequalities, we show that a certain map from the $n$--torus to the space of symplectic embeddings from one ellipsoid to the other induces an injective map on singular homology with mod $2$ coefficients. The proof uses parametrized moduli spaces of $J$--holomorphic cylinders in completed symplectic cobordisms. 



Noncontractible loops of symplectic embeddings between convex toric domains

  • M. Munteanu
  • Mathematics
    Journal of Symplectic Geometry
  • 2020
Given two 4-dimensional ellipsoids whose symplectic sizes satisfy a specified inequality, we prove that a certain loop of symplectic embeddings between the two ellipsoids is noncontractible. The

Symplectormophism groups of non-compact manifolds, orbifold balls, and a space of Lagrangians

We establish connections between contact isometry groups of certain contact manifolds and compactly supported symplectomorphism groups of their symplectizations. We apply these results to investigate

Symplectic capacities from positive S1–equivariant symplectic homology

We use positive S^1-equivariant symplectic homology to define a sequence of symplectic capacities c_k for star-shaped domains in R^{2n}. These capacities are conjecturally equal to the Ekeland-Hofer

Symplectic embeddings of products

McDuff and Schlenk determined when a four-dimensional ellipsoid can be symplectically embedded into a four-dimensional ball, and found that when the ellipsoid is close to round, the answer is given

Compactness results in Symplectic Field Theory

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The Hofer conjecture on embedding symplectic ellipsoids

In this note we show that one open four dimensional ellipsoid embeds symplectically into another if and only the ECH capacities of the first are no larger than those of the second. This proves a

Coherent orientations in symplectic field theory

Abstract.We study the coherent orientations of the moduli spaces of holomorphic curves in Symplectic Field Theory, generalizing a construction due to Floer and Hofer. In particular we examine their

Lectures on Symplectic Field Theory

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In determining when a four‐dimensional ellipsoid can be symplectically embedded into a ball, McDuff and Schlenk found an infinite sequence of ‘ghost’ obstructions that generate an infinite ‘ghost

Pseudo holomorphic curves in symplectic manifolds

Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is called