Finite group actions on bordered surfaces of small genus |
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Authors: | E. Bujalance M.D.E. Conder |
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Affiliation: | a Dep. Matemáticas Fundamentales, Fac. Ciencias, UNED, Senda del Rey 9, 28040 Madrid, Spain b Department of Mathematics, University of Auckland, Private Bag 92019 Auckland 1142, New Zealand c Institute of Mathematics, University of Gdańsk, ul. Wita Stwosza 57, 80-952 Gdańsk, Poland |
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Abstract: | 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. |
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Keywords: | 30F50 57M6 20H10 |
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