On topological type of periodic self-homeomorphisms of closed non-orientable surfaces

Let S g denote a closed non-orientable surface of genus g ≥ 3 . At the beginning of 1980s E. Bujalance showed that the maximum order of a periodic self-homeomorphism of S g is equal to 2 g or 2 ( g - 1 ) for g odd or even respectively, and this upper bound is attained for all g ≥ 3 . In this paper w...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2016-09, Vol.110 (2), p.303-320
Main Authors: Gromadzki, G., Szepietowski, B.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Conjugation
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Quotients
Texts
Theoretical
Topology
Upper bounds
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Summary:Let S g denote a closed non-orientable surface of genus g ≥ 3 . At the beginning of 1980s E. Bujalance showed that the maximum order of a periodic self-homeomorphism of S g is equal to 2 g or 2 ( g - 1 ) for g odd or even respectively, and this upper bound is attained for all g ≥ 3 . In this paper we enumerate, up to topological conjugation, actions on S g of a cyclic group Z N of order N > g - 2 with prescribed type of the quotient orbifold S g / Z N . We also compute, for a fixed g and N ranging between max { g , 3 ( g - 2 ) / 2 } and 2 g , the total numbers of different topological types of action of Z N on S g .
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-015-0234-6