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DISCRETE PRESENTATIONS OF THE HOLONOMY GROUP OF A ONE-HOLED TORUS

김홍찬
한국수학교육학회|2010.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제17권 제4호|pp. 275-288

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참고문헌

키워드

discretenessa one-holed torushyperbolic structureholonomy group
주제분류수학

초록

A one-holed torus §(1; 1) is a building block of oriented surfaces. In this paper we formulate the matrix presentations of the holonomy group of a one-holed torus §(1; 1) by the gluing method. And we present an algorithm for deciding the discreteness of the holonomy group of §(1; 1).

Abstract

A one-holed torus §(1; 1) is a building block of oriented surfaces. In this paper we formulate the matrix presentations of the holonomy group of a one-holed torus §(1; 1) by the gluing method. And we present an algorithm for deciding the discreteness of the holonomy group of §(1; 1).

참고문헌 (11)

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  6. 김홍찬, "Discrete conditions for the holonomy group of a pair of pants", 대한수학회지, 44(3), pp.615~626 (2007), 대한수학회
  7. N. Kuiper, "On convex locally projective spaces", pp.200~213 (1953), Convegno Internazionale di Geometria Differenziale
  8. K. Matsuzaki, "Hyperbolic manifolds and Kleinian groups" (1998), Oxford Sci-ence Publications, Oxford University Press
  9. D. Sullivan, "Manifolds with canonical coordinates: Some examples", Enseign. Math, 29, pp.15~25 (1983)
  10. W. Thurston, "Three-dimensional geometry and topology Vol. 1" (1997), Princeton University Press
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