On the xed-point set of automorphisms of non-orientable surfaces without boundary
نویسندگان
چکیده
Macbeath gave a formula for the number of xed points for each non-identity element of a cyclic group of automorphisms of a compact Riemann surface in terms of the universal covering transformation group of the cyclic group. We observe that this formula generalizes to determine the xed-point set of each non-identity element of a cyclic group of automorphisms acting on a closed non-orientable surface with one exception; namely, when this element has order 2. In this case the xed-point set may have simple closed curves (called ovals) as well as xed points. In this note we extend Macbeath’s results to include the number of ovals and also determine whether they are twisted or not. AMS Classi cation 20F10, 30F10; 30F35, 51M10, 14H99
منابع مشابه
On the fixed-point set of automorphisms of non-orientable surfaces without boundary
Macbeath gave a formula for the number of fixed points for each non-identity element of a cyclic group of automorphisms of a compact Riemann surface in terms of the universal covering transformation group of the cyclic group. We observe that this formula generalizes to determine the fixed-point set of each non-identity element of a cyclic group of automorphisms acting on a closed non-orientable...
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