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On the set of fixed points of automorphisms of bordered Klein surfaces


Gamboa, J. M. and Gromadzki, G. (2012) On the set of fixed points of automorphisms of bordered Klein surfaces. Revista Matemática Iberoamericana, 28 (1). pp. 113-126. ISSN 0213-2230


The nature of the set of points fixed by automorphisms of Riemann or unbordered nonorientable Klein surfaces as well as quantitative formulae for them were found by Macbeath, Izquierdo, Singerman and Gromadzki in a series of papers. The possible set of points fixed by involutions of bordered Klein surfaces has been found by Bujalance, Costa, Natanzon and Singerman who showed that it consists of isolated fixed points, ovals and chains of arcs. They classified involutions of such surfaces, up to topological conjugacy in these terms. Here we give formulae for the number of elements of each type, also for non-involutory automorphisms, in terms of the topological type of the action of the group of dianalytic automorphisms. Finally we give some illustrative examples concerning bordered Klein surfaces with large groups of automorphisms already considered by May and Bujalance.

Item Type:Article
Uncontrolled Keywords:Automorphisms of Riemann (Klein) surfaces, symmetries of Riemann surfaces, fixed points, Fuchsian, NEC groups
Subjects:Sciences > Mathematics > Algebra
ID Code:17275
Deposited On:29 Nov 2012 11:40
Last Modified:02 Mar 2016 14:39

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