Examples of non-target-representable symplectic capacities

Abstract

We give the first concrete example of a symplectic capacity that is not target-representable. The capacity is defined on the class of all compact and exact symplectic manifolds. This provides some concrete answer to a question by Cieliebak, Hofer, Latschev, and Schlenk.We also show that a capacity on the class of all closed symplectic manifolds is not target-representable, if it is finite at certain symplectic manifolds. In particular, the Hofer-Zehnder capacity on the class of all closed symplectic manifolds is not target-representable.