Homotopic curves on surfaces
Homotopic curves on surfaces
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曲面上的同伦曲线
DOI：
10.1090/s0002-9939-1963-0157364-3
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发表时间：
1963
期刊：
影响因子：
--
通讯作者：
H. Levine
中科院分区：
文献类型：
--
作者：
H. Levine
在下文中，曲面总是紧凑的、可定向的、有边界或无边界的二维流形，闭合曲面是没有边界的曲面，曲面上的简单闭合曲线是闭合的、连通的一维子流形。为了简单地引用曲线，在圆的嵌入和嵌入下的图像之间没有符号上的区别-上下文将清楚地表明哪一个是想要的。如果W是一个边界由n条不相交的简单闭合曲线组成的曲面，则W的亏格g(W)被定义为没有边界的曲面的亏格，它是通过在每条边界曲线上附加一个2-胞元而得到的。W的亏格与其内欧拉特征x(W)之间的关系为：
In the following, a surface is always a compact, orientable, twodimensional manifold with or without boundary, a closed surface is one without boundary, and a simple, closed curve on a surface is a closed, connected, one-dimensional submanifold. For simplicity in referring to curves, no notational distinction is made between the embedding of the circle and the image under the embedding-the context will make it clear which is intended. If W is a surface whose boundary consists of n disjoint, simple, closed curves, the genus of W, g(W), is defined to be the genus of a surface without boundary obtained by attaching a 2-cell to each of the boundary curves. The relation between the genus of W and its inner Euler characteristic, x(W) is: