Automorphisms and coverings of Klein surfaces
Hall, Wendy(1977)Automorphisms and coverings of Klein surfaces.University of Southampton,Maths,Doctoral Thesis.
Abstract
In this thesis the theory of automorphisms and coverings of compact Klein surfaces is discussed by considering a Klein surface as the orbit space of a non-Euclidean crystallographic group. In chapter 1 we set out some of the well-established theory concerning these ideas. In chapter 2 maximal automorphism groups of compact Klein surfaces without boundary are considered. We solve the problem of which groups PSL (2,q) act as maximal automorphism groups of non-orientable Klein surface without boundary. In chapter 3 we discuss cyclic groups acting as automorphism groups of compact Klein surfaces without boundary. It is shown that the maximum order for a cyclic group to be an automorphism group of a compact non-orientable Klein surface without boundary of genus g ?3 is 2g, if g is odd and 2 (g – 1) if g is even. Chapter 4 is the largest section of the thesis. It is concerned with coverings (possibly folded and ramified) of compact Klein surfaces, mainly Klein surfaces with boundary. All possible two-sheeted connected unramified covering surfaces of a Klein surface are classified and the orientability of a normal n-sheeted cover, for odd n, is determined
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