Involve: A Journal of Mathematics
- Volume 8, Number 4 (2015), 665-676.
On symplectic capacities of toric domains
A toric domain is a subset of which is invariant under the standard rotation action of on . For a toric domain from a certain large class for which this action is not free, we find a corresponding toric domain where the standard action is free and for which for any symplectic capacity . Michael Hutchings gives a combinatorial formula for calculating his embedded contact homology symplectic capacities for certain toric four-manifolds on which the -action is free. Our theorem allows one to extend this formula to a class of toric domains where the action is not free. We apply our theorem to compute ECH capacities for certain intersections of ellipsoids and find that these capacities give sharp obstructions to symplectically embedding these ellipsoid intersections into balls.
Involve, Volume 8, Number 4 (2015), 665-676.
Received: 20 June 2014
Revised: 30 July 2014
Accepted: 2 August 2014
First available in Project Euclid: 22 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Landry, Michael; McMillan, Matthew; Tsukerman, Emmanuel. On symplectic capacities of toric domains. Involve 8 (2015), no. 4, 665--676. doi:10.2140/involve.2015.8.665. https://projecteuclid.org/euclid.involve/1511370917