A Lower Bound of the Hofer-Zehnder Capacity via Delzant Polytopes

2023/12/15 by Liu, Yichen
#53D20 #53D35 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2312.09526

Abstract

Given a symplectic toric manifold, the moment maps of sub-circle actions can be modified to be admissible functions in the sense of Hofer-Zehnder. By exploiting the relationship between the period of Hamiltonian sub-circle actions of a symplectic toric manifold and its Delzant polytope, we develop an invariant of Delzant polytopes which gives a lower bound of the Hofer-Zehnder capacity.

Related

• Hofer-Zehnder semicapacity of cotangent bundles and symplectic submanifolds
• Kahler geometry of toric manifolds in symplectic coordinates
• Hofer-Zehnder capacity and a Hamiltonian circle action with noncontractible orbits
• Symplectic capacities from Hamiltonian circle actions
• Moment polytopes for symplectic manifolds with monodromy