科研之友
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摘要
A faithful action of a group G on the genus g > 1 orientable closed surface Sigma(g) is extendable (over the three-dimensional sphere S-3), with respect to an embedding e : Sigma(g hooked right arrow) S-3, if there is an action of G on S-3 such that h omicron e = e omicron h for any h is an element of G. We show that the maximum order of extendable cyclic group actions on Sigma(g) is 4g + 4 when g is even, and 4g - 4 when g is odd; the maximum order of extendable abelian group actions on Sigma(g) is 4g + 4. We also give the maximum orders of cyclic and abelian group actions on handlebodies.
- 出版日期2018
- 单位吉林大学
