Structures of geometric quotient orbifolds of three-dimensional G-manifolds of genus two
1
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
In this article, we will characterize structures of geometric quotient orbifolds of G-manifold of genus two where G is a finite group of orientation preserving diffeomorphisms using the idea of handlebody orbifolds. By using the characterization, we will deduce the candidates of possible non-hyperbolic geometric quotient orbifolds case by case using W. Dunbar's work. In addition, if the G-manifold is compact, closed and the quotient orbifold's geometry is hyperbolic then we can show that the fundamental group of the quotient orbifold cannot be in the class D.
Abstract
In this article, we will characterize structures of geometric quotient orbifolds of G-manifold of genus two where G is a finite group of orientation preserving diffeomorphisms using the idea of handlebody orbifolds. By using the characterization, we will deduce the candidates of possible non-hyperbolic geometric quotient orbifolds case by case using W. Dunbar's work. In addition, if the G-manifold is compact, closed and the quotient orbifold's geometry is hyperbolic then we can show that the fundamental group of the quotient orbifold cannot be in the class D.
참고문헌 (9)
- M. Boileau, "Nombre de ponts et g´en´erateurs m´eridiens des entrelacs de Montesinos", Comment. Math. Helv., 60, pp.270~279 (1985)
- W. D. Dunbar, "Geometric orbifolds", Rev. Mat. Univ. Complut. Madrid, 1(1), pp.67~99 (1988)
- E. Klimenko, "Two-generator Kleinian orbifolds", ~
- T. Kobayashi, "Structures of the Haken manifolds with Heegaard splittings of genus two", Osaka J. Math., 21(2), pp.437~455 (1984)
- D. McCullough, "Group actions on handlebodies", Proc. London Math. Soc., 59(2), pp.373~416 (1989)
- W. H. Meeks, "The equivariant loop theorem for three-dimensional manifolds and a review of the existence theorems for minimal surfaces, The Smith conjecture", Pure Appl. Math., 112 (1984), Academic Press
- A. Miller, "Large groups of symmetries of handlebodies", Proc. Amer. Math. Soc., 106(3), pp.829~838 (1989)
- J. P. Serre, "Trees" (2003), Springer-Verlag
- B. Zimmermann, "Genus actions of finite groups on 3-manifolds", Michigan Math. J., 43(3), pp.593~610 (1996)