## Involve: A Journal of Mathematics

• Involve
• Volume 8, Number 4 (2015), 665-676.

### On symplectic capacities of toric domains

#### Abstract

A toric domain is a subset of $(ℂn,ωstd)$ which is invariant under the standard rotation action of $Tn$ on $ℂn$. For a toric domain $U$ from a certain large class for which this action is not free, we find a corresponding toric domain $V$ where the standard action is free and for which $c(U) = c(V )$ for any symplectic capacity $c$. Michael Hutchings gives a combinatorial formula for calculating his embedded contact homology symplectic capacities for certain toric four-manifolds on which the $T2$-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.

#### Article information

Source
Involve, Volume 8, Number 4 (2015), 665-676.

Dates
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
https://projecteuclid.org/euclid.involve/1511370917

Digital Object Identifier
doi:10.2140/involve.2015.8.665

Mathematical Reviews number (MathSciNet)
MR3366017

Zentralblatt MATH identifier
1322.53081

#### Citation

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

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