Hyperelliptic Klein surfaces with maximal symmetry



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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
ID Code:15751
Deposited On:25 Jun 2012 09:43
Last Modified:25 Jun 2012 09:43

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