On automorphism groups of Riemann double covers of Klein surfaces

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• 作者：E. Bujalance^a ; ¹ ; ^{eb@mat.uned.es} ; F.J. Cirre^a ; ¹ ; ^{jcirre@mat.uned.es} ; M.D.E. Conder^b ; ² ; ^{m.conder@auckland.ac.nz}
• 关键词：Automorphisms ; Riemann surfaces ; Fuchsian groups ; Klein surfaces ; Non-Euclidean crystallographic groups
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：472
• 期：Complete
• 页码：146-171
• 全文大小：543 K
• 卷排序：472

文摘

If G is a group of automorphisms of a compact Klein surface X  , then the direct product G×C2G×C2 is a group of automorphisms of the Riemann double cover X+X+ of X. In this paper we analyse the relationship between G   and the full groups of automorphisms Aut(X)Aut(X) and Aut(X+)Aut(X+) of X   and X+X+ respectively, in the special case where the group G   is uniformised by a non-Euclidean crystallographic group with quadrangular signature (2,2,2,n)(2,2,2,n). There is a difference in what happens between bordered surfaces and unbordered non-orientable surfaces, and so we consider those cases separately (including the special situation for n=4n=4 in the unbordered case).