兰州大学机构库 >数学与统计学院
柏拉图多面体链环新欧拉示性数与亏格的研究
Alternative TitleThe Research of Platonic Polyhedral links`New Euler Characteristics and Genus
时晓萌
Thesis Advisor邱文元
2013-05-18
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword新欧拉公式 奇偶次交错缠绕 欧拉示性数 亏格
Abstract本文以Seifert构造为基础,在柏拉图多面体上设计奇偶次交错缠绕的非等边多面体链环,得到了新欧拉公式的示性数及亏格公式。首先对含有不同的奇偶次缠绕的非等边柏拉图多面体链环进行定向,通过Seifert构造的方法计算其Seifert环数s,同时计算出交叉点数c和分支数μ,当非等边柏拉图多面体链环的奇数次缠绕的边数φ在一定范围内时,可以得出一个普遍意义上的新欧拉公式,即s+μ-c=2-2[( 2kE⁄F-1)∙n+φ],进而得到此时多面体链环的亏格数为(2kE⁄F-1)∙n+φ,其中n=⌈Fφ⁄2E⌉。这一构造方法不仅提出了柏拉图多面体链环在非等边奇偶次交错缠绕下的新欧拉示性数和亏格的计算公式,还为我们研究更为复杂的多面体链环的新欧拉示性数和亏格提供了思路。
Other AbstractA new design in the case of odd and even interlacing to study polyhedral links, and obtained the characteristics and genus with new Euler formula of the un-equilateral polyhedral link. First of all, we give an orientation to the un-equilateral Platonic polyhedral link with different odd and even interlace. Then calculate the Seifert circles s based on the Seifert construction, also the numbers of components μ and crossings c at the same time. When an odd number of twists φ of the un-equilateral Platonic polyhedral link changes within a certain range, we gained a new Euler formula, which has general meaning is s+μ-c=2-2[( 2kE⁄F-1)∙n+φ], and then get the genus of polyhedral link is (2kE⁄F-1)∙n+φ. This constructor method not only provides the new method on the new Euler characteristic and the computational formula of genus in the un-equilateral polyhedral link, but also provides new ideas to research the new Euler characteristic and genus which more complicated.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225634
Collection数学与统计学院
Recommended Citation
GB/T 7714
时晓萌. 柏拉图多面体链环新欧拉示性数与亏格的研究[D]. 兰州. 兰州大学,2013.
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