Involutions of compact Klein surfaces

Symmetry types of hyperelliptic Riemann surfaces

“…Other results concerning topological properties of symmetries of Riemann surfaces have been obtained by Bujalance, Costa, Natanzon and Singerman in [13], Bujalance and Costa in [11] and Izquierdo and Singerman in [34].…”

Doubles of Klein Surfaces

“…an anticonformal involution.) An analogous thing happens for Klein surfaces [2]. We define the Schottky double of X to be a Klein surfaceX without boundary of the same orientability as X admitting a dianalytic involution h whose fixed curves separateX and such thatX/ h =X.…”

On the fixed-point set of automorphisms of non-orientable surfaces without boundary

“…By results in [2] (see also [3]), r is the number of isolated fixed points of t N and is given by Macbeath's formula…”

“…It also follows from [2] that the number of ovals of t N is just the number s of period cycles in Λ, which corresponds to the number of conjugacy classes of reflections in Λ. As a reflection c j in Λ belongs also to Γ and the group Γ has k conjugacy classes of reflections, we just have to determine into how many Λ-conjugacy classes the Γ-conjugacy class of c j splits.…”

“…In [6] (also see [2]) Scherrer showed that that if an involution of a non-orientable surface of genus p has | F | fixed points and | V | ovals then…”