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

Yichen Liu

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

Symplectic Geometry 2024-10-15 v2

Authors: Yichen Liu

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.

Keywords

Hofer-Zehnder capacity Delzant polytopes symplectic toric manifold moment map Hamiltonian action

Cite

@article{arxiv.2312.09526,
  title  = {A Lower Bound of the Hofer-Zehnder Capacity via Delzant Polytopes},
  author = {Yichen Liu},
  journal= {arXiv preprint arXiv:2312.09526},
  year   = {2024}
}

Comments

12 pages, 3 figures, comments are welcome! Version 2 has a minor mistake fixed and includes more references for relavant work

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