Journal of Symplectic Geometry

Packing numbers of rational ruled four-manifolds

Olguta Buse and Martin Pinsonnault

Full-text: Open access


We completely solve the symplectic packing problem with equally sized balls for any rational, ruled, symplectic four-manifolds. We give explicit formulae for the packing numbers, the generalized Gromov widths, the stability numbers, and the corresponding obstructing exceptional classes. As a corollary, we give explicit values for when an ellipsoid of type $E(a, b)$, with $\frac{b}{a} \in \mathbb{N}$, embeds in a polydisc $P(s,t)$. Under this integrality assumption, we also give an alternative proof of a recent result of M. Hutchings showing that the embedded contact homology capacities give sharp inequalities for embedding ellipsoids into polydisks.

Article information

J. Symplectic Geom., Volume 11, Number 2 (2013), 269-316.

First available in Project Euclid: 11 November 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Buse, Olguta; Pinsonnault, Martin. Packing numbers of rational ruled four-manifolds. J. Symplectic Geom. 11 (2013), no. 2, 269--316.

Export citation