Maximum orders of extendable actions on surfaces

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• 作者：Chao Wang ; Shi Cheng Wang ; Yi Mu Zhang
• 关键词：Symmetry of surface ; symmetry of 3 ; sphere ; extendable action ; 57M60 ; 57S17 ; 57S25
• 刊名：Acta Mathematica Sinica
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：32
• 期：1
• 页码：54-68
• 全文大小：435 KB
• 参考文献：[1]Boileau, M., Maillot, S., Porti, J.: Three-dimensional orbifolds and their geometric structures. Panoramas et Synthses, 15, Socit Mathmatique de France, Paris, 2003
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  [5]Perelman, G.: The entropy formula for the Ricci flow and its geometric applications, Ricci flow with surgery on three-manifolds, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, arXiv: math.DG/0211159, math.DG/0303109, math.DG/0307245.
  [6]Thurston, W.: Three dimensional manifolds, Kleinian groups and hyperbolic geometry. Bull. Amer. Math. Soc., 316, 357鈥?81 (1982)CrossRef MathSciNet
  [7]Wang, C., Wang, S. C., Zhang, Y. M., et al.: Extending finite group actions on surfaces over S 3. Topology Appl., 160, 2088鈥?103 (2013)CrossRef MathSciNet MATH
  [8]Wang, C., Wang, S. C., Zhang, Y. M., et al.: Embedding surfaces into S 3 with maximum symmetry, arXiv:1209.1170 math.GT (math.CO math.GR), accepted by Groups, Geometry, and Dynamics
  
• 作者单位：Chao Wang (1)
  Shi Cheng Wang (1)
  Yi Mu Zhang (1)
  
  1. School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-published
• ISSN：1439-7617

文摘

We determine the maximum order E _g of finite groups G acting on the closed surface 危 _g of genus g which extends over (S 3,危 _g ) for all possible embeddings 危 _g 鈫?S 3, where g > 1. Keywords Symmetry of surface symmetry of 3-sphere extendable action