Maximum Orders of Cyclic and Abelian Extendable Actions on Surfaces

2013/10/28 by Wang, Chao, Zhang, Yimu
#57M60 #57S17 #57S25 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1310.7302

Abstract

Let Σ_g (g>1) be a closed surface embedded in S³. If a group G can acts on the pair (S³, Σ_g), then we call such a group action on Σ_g extendable over S³. In this paper we show that the maximum order of extendable cyclic group actions is 4g+4 when g is even and 4g-4 when g is odd; the maximum order of extendable abelian group actions is 4g+4. We also give results of similar questions about extendable group actions over handlebodies.

Related

• Extending finite group actions on surfaces over S³
• Embedding surfaces into S³ with maximum symmetry
• Extendability of group actions on K3 or Enriques surfaces
• Bordered surfaces in the 3-sphere with maximum symmetry
• The Alternating Groups and K3 Surfaces