arXiv subjects

Jonathan Trejos

Publications and source records attributed to Jonathan Trejos.

3 recordsLinked to original sources

arXiv2026

Obstruction to Symplectic Embeddings between Toric Domains

We study symplectic embeddings between four-dimensional toric domains using embedded contact homology. Extending Hutchings' criterion for embeddings between convex toric domains, we obtain obstructions for embeddings from convex toric domains into concave toric domains, from semi-weakly convex toric domains into convex toric domains, and from concave toric domains into concave toric domains. The obstructions are formulated in terms of factorizations of convex, concave, and semi-weakly convex generators together with combinatorial constraints relating their ECH indices and actions. As applications, we recover the sharp obstruction for symplectic embeddings of a polydisk into a union of cylinders, and obtain sharp results for embeddings of certain quadrilateral toric domains into balls and ellipsoids. We also show that these obstructions are in some cases strictly stronger than those coming only from ECH capacities.

math.SG↗

arXiv2025

ECH capacities of concave singular toric domains

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 diffeomorphic to a lens space L(n, 1). We call them 'singular toric domains' since they naturally have an orbifold point. We calculate the ECH capacities for a specific subfamily of these singular toric domains that generalize the concave toric domains. Interestingly, even though we are calculating the capacities of an orbifold, the result can be adapted to study embedding problems in some of the desingularizations of these spaces, for example the unitary cotangent bundle of two dimensional sphere or the unitary cotangent bundle of projective plane.

math.SG↗

arXiv2023

Symplectic embeddings of toric domains with boundary a lens space

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 concave toric domain in a way that possesses a singularity point and has a boundary a lens space. After desingularization these toric domains include the unitary cotangent bundle of $\mathbb{S}^2$ and the unitary cotangent bundle of $\mathbb{R}P^2$. We use the combinatorial expression of the ECC to compute the ECH capacities of these toric domains. Furthermore, for certain concave toric domains we describe a packing of symplectic manifolds that recovers their ECH capacities.

math.SG↗