# Symplectic embeddings into disk cotangent bundles

@inproceedings{Ferreira2021SymplecticEI, title={Symplectic embeddings into disk cotangent bundles}, author={Brayan Ferreira and Vinicius G. B. Ramos}, year={2021} }

In this paper, we compute the embedded contact homology (ECH) capacities of the disk cotangent bundles D∗S2 and D∗RP 2. We also find sharp symplectic embeddings into these domains. In particular, we compute their Gromov widths. In order to do that, we explicitly calculate the ECH chain complexes of S∗S2 and S∗RP 2 using a direct limit argument on the action inspired by Bourgeois’s Morse–Bott approach and ideas from Nelson–Weiler’s work on the ECH of prequantization bundles. Moreover, we use…

## References

SHOWING 1-10 OF 57 REFERENCES

An index inequality for embedded pseudoholomorphic curves in symplectizations

- Mathematics
- 2001

Abstract.Let Σ be a surface with a symplectic form, let φ be a symplectomorphism of Σ, and let Y be the mapping torus of φ. We show that the dimensions of moduli spaces of embedded pseudoholomorphic…

Symplectic embeddings and the lagrangian bidisk

- Mathematics
- 2017

In this paper we obtain sharp obstructions to the symplectic embedding of the lagrangian bidisk into four-dimensional balls, ellipsoids and symplectic polydisks. We prove, in fact, that the interior…

Symplectic embeddings from concave toric domains into convex ones

- MathematicsJournal of Differential Geometry
- 2019

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",…

Embedded contact homology of prequantization bundles

- Mathematics
- 2020

The 2011 PhD thesis of Farris demonstrated that the ECH of a prequantization bundle over a Riemann surface is isomorphic as a Z/2Z-graded group to the exterior algebra of the homology of its base. We…

Symplectic embeddings into four‐dimensional concave toric domains

- Mathematics
- 2013

ECH (embedded contact homology) capacities give obstructions to symplectically embedding one symplectic four‐manifold with boundary into another. We compute the ECH capacities of a large family of…

Quantitative embedded contact homology

- Mathematics
- 2010

Define a "Liouville domain" to be a compact exact symplectic manifold with contact-type boundary. We use embedded contact homology to assign to each four-dimensional Liouville domain (or subset…

The embedded contact homology index revisited

- Mathematics
- 2008

Let Y be a closed oriented 3-manifold with a contact form such that all Reeb orbits are nondegenerate. The embedded contact homology (ECH) index associates an integer to each relative 2-dimensional…

Reeb dynamics inspired by Katok’s example in Finsler geometry

- Mathematics
- 2017

Inspired by Katok’s examples of Finsler metrics with a small number of closed geodesics, we present two results on Reeb flows with finitely many periodic orbits. The first result is concerned with a…

Algebraic Torsion in Higher-Dimensional Contact Manifolds

- Mathematics
- 2019

We construct examples in any odd dimension of contact manifolds with finite and non-zero algebraic torsion (in the sense of Latschev-Wendl), which are therefore tight and do not admit strong…

Rounding corners of polygons and the embedded contact homology of T 3

- Mathematics
- 2006

The embedded contact homology (ECH) of a 3‐manifold with a contact form is a variant of Eliashberg‐Givental‐Hofer’s symplectic field theory, which counts certain embedded J ‐holomorphic curves in the…