局部接触同调及其应用
辛几何
2013-09-24 v3 动力系统
摘要
我们为Reeb流的孤立周期轨道引入了局部版本的接触同调，并证明其秩在孤立迭代中一致有界。获得了若干应用，包括Gromoll-Meyer定理关于无穷多简单周期轨道存在的推广、共振关系以及非双曲周期轨道存在的条件。
引用
@article{arxiv.1202.3122,
title = {Local contact homology and applications},
author = {Umberto Hryniewicz and Leonardo Macarini},
journal= {arXiv preprint arXiv:1202.3122},
year = {2013}
}
备注
62 pages. We would like to thank Michael Hutchings for pointing out a problem in our previous attempt to define local contact homology using domain-dependent almost complex structures. For more details see http://floerhomology.wordpress.com/2013/09/08/an-obstruction-to-cylindrical-contact-homology/