论文标题
奇异化对欧拉特征的影响
The Effect of Singularization on the Euler Characteristic
论文作者
论文摘要
在这项工作中，通过应用三个基本的简单循环操作，折叠操作，拉链操作和双环识别来获得单数表面，从平滑的可定向闭合表面获得，每个表面都会产生不同的奇异表面。证明了提供奇异表面的欧拉特性的公式。另外，我们引入了一个新的属属的定义，该属属地表面概括了平滑案例中对属的经典定义。证明了与奇异表面属有关的定理。
In this work, singular surfaces are obtained from smooth orientable closed surfaces by applying three basic simple loop operations, collapsing operation, zipping operation and double loop identification, each of which produces different singular surfaces. A formula that provides the Euler characteristic of the singularized surface is proved. Also, we introduce a new definition of genus for singularized surfaces which generalizes the classical definition of genus in the smooth case. A theorem relating the Euler characteristic to the genus of the singularized surface is proved.
