Related papers: Refined Elementary Capacities from Symplectic Fiel…
We use explicit pseudoholomorphic curve techniques (without virtual perturbations) to define a sequence of symplectic capacities analogous to those defined recently by the second named author using symplectic field theory. We then compute…
We establish computational results concerning the Lagrangian capacity from "Cieliebak and Mohnke - Punctured holomorphic curves and Lagrangian embeddings". More precisely, we show that the Lagrangian capacity of a 4-dimensional convex toric…
We present recursive formulas which compute the recently defined "higher symplectic capacities" for all convex toric domains. In the special case of four-dimensional ellipsoids, we apply homological perturbation theory to the associated…
ECH capacities give obstructions to symplectically embedding one symplectic four-manifold with boundary into another. We compute the ECH capacities of a large family of symplectic four-manifolds with boundary, called "concave toric…
The ECH capacities are a sequence of numerical invariants of symplectic four-manifolds which give (sometimes sharp) obstructions to symplectic embeddings. These capacities are defined using embedded contact homology, and establishing their…
We initiate the study of the rational SFT capacities of Siegel using tools in toric algebraic geometry. In particular, we derive new (often sharp) bounds for the RSFT capacities of a strongly convex toric domain in dimension $4$. These…
Embedded contact homology gives a sequence of obstructions to four-dimensional symplectic embeddings, called ECH capacities. In "Symplectic embeddings into four-dimensional concave toric domains", the author, Choi, Frenkel, Hutchings and…
A toric domain is a subset of $(\mathbb{C}^n,\omega_{\text{std}})$ which is invariant under the standard rotation action of $\mathbb{T}^n$ on $\mathbb{C}^n$. For a toric domain $U$ from a certain large class for which this action is not…
The ECH capacities are a sequence of real numbers associated to any symplectic four-manifold, which are monotone with respect to symplectic embeddings. It is known that for a compact star-shaped domain in R^4, the ECH capacities…
A strong version of a conjecture of Viterbo asserts that all normalized symplectic capacities agree on convex domains. We review known results showing that certain specific normalized symplectic capacities agree on convex domains. We also…
ECH capacities are rich obstructions to symplectic embeddings in 4-dimensions that have also been seen to arise in the context of algebraic positivity for (possibly singular) projective surfaces. We extend this connection to relate general…
ECH (embedded contact homology) capacities give obstructions to symplectically embedding one four-dimensional symplectic manifold with boundary into another. These obstructions are known to be sharp when the domain and target are ellipsoids…
We study the related notions of curvature and perimeter for toric boundaries and their implications for symplectic packing problems; a natural setting for this is a generalized version of convex toric domain which we also study, where there…
ECH capacities were developed by Hutchings to study embedding problems for symplectic $4$-manifolds with boundary. They have found especial success in the case of certain toric symplectic manifolds where many of the computations resemble…
We give a combinatorial description of the embedded contact complex (ECC) of a certain family of contact toric lens spaces that we call concave lens spaces. We also define a notion of a concave toric domain that generalizes the usual…
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 capacities, but they satisfy axioms which…
By definition, a toric domain has a boundary contact manifold diffeomorphic to a three dimensional sphere. In the present work we extend the definition of the toric domains in dimension four so that it admits a contact manifold…
We construct new families of symplectic capacities indexed by certain symmetric polynomials, defined using rational symplectic field theory. In particular, we introduce a sequence of capacities based on an L-infinity structure on linearized…
We establish computational results concerning the Lagrangian capacity, originally defined by Cieliebak-Mohnke. More precisely, we show that the Lagrangian capacity of a 4-dimensional convex toric domain is equal to its diagonal. Working…
Let $X$ be a union of a sequence of symplectic manifolds of increasing dimension and let $M$ be a manifold with a closed $2$-form $\omega$. We use Tischler's elementary method for constructing symplectic embeddings in complex projective…