迈向无限型曲面的 Nielsen-Thurston 分类
几何拓扑
2023-10-19 v2
摘要
我们引入并研究无限型曲面的驯良同胚。这类映射在迭代下曲线不会累积到具有非真叶的测地叶状结构上，而仅累积为可能相交的曲线或真直线的并。在累积集上附加有限性条件后，我们证明了一种 Nielsen-Thurston 型分类定理。我们证明，对此类映射，曲面可典范分解为不变子曲面，其上的首次返回映射或为周期，或为平移。
引用
@article{arxiv.2303.12413,
title = {Towards Nielsen-Thurston classification for surfaces of infinite type},
author = {Mladen Bestvina and Federica Fanoni and Jing Tao},
journal= {arXiv preprint arXiv:2303.12413},
year = {2023}
}
备注
Main modifications: conjecture updated and changes in some definitions and proofs relating to subsurfaces. Section 5 in v1 is now split into sections 5 and 6. New examples added