Topology of Stable Maps of Surfaces with Boundary into the Plane
Topology of Stable Maps of Surfaces with Boundary into the Plane
复制标题
平面内边界稳定曲面图的拓扑
DOI：
10.1007/s00574-022-00304-w
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Yamamoto Takahiro
中科院分区：
文献类型：
--
作者：
Kitazawa Naoki;Saeki Osamu;山田真希子;櫻木麻衣・梅田 聡;山田真希子;品川和志・石川直樹・梅田 聡;Yamamoto Takahiro
设为具有一个边界分支的连通紧致定向曲面。如果它的局部行为类似于M的边界邻域上的稳定映射，则它是弱可容许的。引入了弱可容映射的半边界缠绕数和弱可容映射之间的弱可容同伦的概念。然后，我们证明了弱容许映射和弱容许同伦的充要条件是半边界缠绕数与的半边界缠绕数一致。此外，我们还引入了一个关于稳定映射的亏格M的公式。
LetMbe a connected compact oriented surface with one boundary component. Amapisweakly admissibleif it behaves locally like a stable map on a neighbourhood of the boundaryofM. The notions of the half boundary winding number of a weakly admissiblemapand weakly-admissibly homotopic among weakly admissiblemapsare introduced. Then, we show that weakly admissiblemapsandare weakly-admissibly homotopic if and only if the half boundary winding number ofcoincides with that of. Furthermore, we introduce a formula concerning the genusgofMfor a stable map.