Finite group actions on bordered surfaces of small genus

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• 作者：E. Bujalance ; F.J. Cirre ; M.D.E. Conder ; B. Szepietowski
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2010
• 出版时间：December 2010
• 年：2010
• 卷：214
• 期：12
• 页码：2165-2185
• 全文大小：541 K

文摘

This paper considers finite group actions on compact bordered surfaces — quotients of unbordered orientable surfaces under the action of a reflectional symmetry. Classification of such actions (up to topological equivalence) is carried out by means of the theory of non-euclidean crystallographic groups, and determination of normal subgroups of finite index in these groups, up to conjugation within their automorphism group. A result of this investigation is the determination, up to topological equivalence, of all actions of groups of finite order 6 or more on compact (orientable or non-orientable) bordered surfaces of algebraic genus p for 2≤p≤6. We also study actions of groups of order less than 6, or of prime order, on bordered surfaces of arbitrary algebraic genus p≥2.