Open Access
Translator Disclaimer
2015 On symplectic capacities of toric domains
Michael Landry, Matthew McMillan, Emmanuel Tsukerman
Involve 8(4): 665-676 (2015). DOI: 10.2140/involve.2015.8.665


A toric domain is a subset of (n,ωstd) which is invariant under the standard rotation action of Tn on n. 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.


Download Citation

Michael Landry. Matthew McMillan. Emmanuel Tsukerman. "On symplectic capacities of toric domains." Involve 8 (4) 665 - 676, 2015.


Received: 20 June 2014; Revised: 30 July 2014; Accepted: 2 August 2014; Published: 2015
First available in Project Euclid: 22 November 2017

zbMATH: 1322.53081
MathSciNet: MR3366017
Digital Object Identifier: 10.2140/involve.2015.8.665

Primary: 53D05 , 53D20 , 53D35

Keywords: moment space axes , symplectic capacities , toric domain

Rights: Copyright © 2015 Mathematical Sciences Publishers


Vol.8 • No. 4 • 2015
Back to Top