泊松流形上哈密顿作用的刚性
辛几何
2012-06-12 v2 微分几何
摘要
本文研究泊松背景下紧群作用的刚性。主要结果是紧半单类型的哈密顿作用是刚性的。我们通过一个针对SCI型闭子群的Nash-Moser正规形定理来证明它。这个Nash-Moser正规形对稳定性结果还有其他应用，我们将在未来的论文中探讨。我们还回顾了紧李群可微作用的一些经典刚性结果，并将其推广到紧李群在辛流形上的辛作用情形。
引用
@article{arxiv.1102.0175,
title = {Rigidity of Hamiltonian actions on Poisson manifolds},
author = {Eva Miranda and Philippe Monnier and Nguyen Tien Zung},
journal= {arXiv preprint arXiv:1102.0175},
year = {2012}
}
备注
41 pages, revised version: minor changes in the statements of Theorems 4.1, 4.6 and 4.7; The proof of Theorem 4.5 has been rewritten; Details have been added in section 6: mainly in the proof of theorem 6.8 and section 6.2.3