This talk is about joint work with Yann Guggisberg. The main result is that the set of generalized symplectic capacities is a complete invariant for every symplectic category whose objects are of the form (M, ω), such that M is compact and 1-connected, ω is exact, and there exists a boundary component of M with negative helicity. This answers a question of Cieliebak, Hofer, Latschev, and Schlenk. It appears to be the first result concerning this question, except for results for manifolds of dimension 2, ellipsoids, and polydiscs in R4.
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