Bujalance, E. and Etayo Gordejuela, J. Javier (1986) Hyperelliptic Klein surfaces with maximal symmetry. In Low Dimensional Topology and Kleinian Groups: Warwick and Durham. London Mathematical Society lecture notes series (112). Cambridge University Press, Cambridge, pp. 289-296. ISBN 0521339057
A Klein surface S is a surface with a dianalytic structure. If S is compact then its underlying topological surface can be orientable or nonorientable and may have boundary. The genus of S is then defined to be the genus of its canonical double which becomes the complex double S ˆ of S when given the canonical complex structure. We call S hyperelliptic if S ˆ is a hyperelliptic Riemann surface. The automorphism group of a Klein surface of genus g is bounded above by 12(g−1) [N. Greenleaf and C. L. May , Trans. Amer. Math. Soc. 274 (1982), no. 1, 265--283]. In the present paper the authors prove that if S is a hyperelliptic Klein surface with 12(g−1) automorphisms then S is homeomorphic to a sphere with 3 holes or a torus with 1 hole. The subspace of Teichmüller space corresponding to these surfaces is briefly considered and shown to consist of submanifolds of dimension 1. The proofs use the algebraic structure of NEC groups.
|Item Type:||Book Section|
|Uncontrolled Keywords:||Fuchsian groups and automorphic functions; Algebraic geometry; Fuchsian groups and their generalizations|
|Subjects:||Sciences > Mathematics > Group Theory|
|Deposited On:||25 Jun 2012 11:43|
|Last Modified:||25 Jun 2012 11:43|
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