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Involutions of compact Klein surfaces. (English) Zbl 0758.30036
Let \(X\) be a compact Klein surface and let \(\varphi: X\to X\) be a dianalytic involution. We determine \(\varphi\) up to topological conjugacy by a finite number of invariants mainly connected with the fixed point set of \(\varphi\).
These results generalize classical results of F. Klein for Riemann surfaces without boundary and of W. Scherrer for non-orientable surfaces without boundary. We investigate corresponding inclusions between non- Euclidean crystallographic groups and use these to consider the spaces of Teichmüller and moduli spaces of Klein surfaces admitting involutions.

MSC:
30F50 Klein surfaces
30F10 Compact Riemann surfaces and uniformization
20H15 Other geometric groups, including crystallographic groups
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References:
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