Work

Examples of non-target-representable symplectic capacities

Year: 2025

Type: article

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.

Source: Differential Geometry and its Applications

DOI: 10.1016/j.difgeo.2025.102309

Authors: Yann Guggisberg, Fabian Ziltener

Institutions: Utrecht University, ETH Zurich

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,740

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek