Vol. 8, No. 4, 2015

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On symplectic capacities of toric domains

Michael Landry, Matthew McMillan and Emmanuel Tsukerman

Vol. 8 (2015), No. 4, 665–676

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.

symplectic capacities, toric domain, moment space axes
Mathematical Subject Classification 2010
Primary: 53D05, 53D20, 53D35
Received: 20 June 2014
Revised: 30 July 2014
Accepted: 2 August 2014
Published: 23 June 2015

Communicated by Michael Dorff
Michael Landry
Mathematics Department
Yale University
10 Hillhouse Avenue
New Haven, CT 06511
United States
Matthew McMillan
Wheaton College
501 College Avenue
Wheaton, IL 60187
United States
Emmanuel Tsukerman
Department of Mathematics
University of California, Berkeley
970 Evans Hall
Berkeley, CA 94720
United States