Fundamental Polygons by Maurice Heins
نویسنده
چکیده
A group © satisfying the hypothesis of Siegel is necessarily of the first kind. The question arises whether there is a theorem of the Siegel type for © of the second kind. I t is one of the objects of the present investigation to establish such a theorem and to draw consequences of this result taken in conjunction with Siegel's theorem. The other object is to study the relation between the parabolic transformations of an unrestricted © and the cusps of an associated noneuclidean convex fundamental polygon (n.e.c.f.p.). To be precise, we understand by this term a set II ( CA) satisfying the following conditions: (1) it is non-euclidean convex, (2) every point of A is ©-equivalent to a point of II, (3) no two distinct points of int II are ©-equivalent, (4) II is closed in the sense of the topology of A, (5) for each point of A there exists a neighborhood intersecting r(II) for only a finite set of T £ @ , (6) (fr II)HA is piecewise hyperbolic rectilinear. The Poincarê polygons are special cases of n.e.c.f.p. We shall refer to n.e.c.f.p. as fundamental polygons.
منابع مشابه
Topological Methods in the Theory of Functions of a Complex Variable Marston Morse and Maurice Heins
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