On periodic self-homeomorphisms of closed orientable surfaces determined by their orders

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• 作者：C. Bagiński ; M. Carvacho ; G. Gromadzki ; R. Hidalgo
• 刊名：Collectanea Mathematica
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：67
• 期：3
• 页码：415-429
• 全文大小：446 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  Analysis
  Applications of Mathematics
  Geometry
  
• 出版者：Springer Milan
• ISSN：2038-4815
• 卷排序：67

文摘

The fundamentals for the topological classification of periodic orientation-preserving self-homeomorphisms of a closed orientable topological surface X of genus \(g \ge 2\) have been established, by Nielsen, in the thirties of the last century. Here we consider two concepts related to this classification; rigidity and weak rigidity. A cyclic action G of order N on X is said to be topologically rigid if any other cyclic action of order N on X is topologically conjugate to it. If this assertion holds for arbitrary other action but having, in addition, the same orbit genus and the same structure of singular orbits, then G is said to be weakly topologically rigid. We give a precise description of rigid and weakly rigid cyclic quasi-platonic actions which mean actions having three singular orbits and for which X / G is a sphere.KeywordsPeriodic self-homeomorphisms of closed orientable surfaces Their classificationRiemann surfacesTheir automorphisms(Real) algebraic curves