INVOLUTIONS AND THE FRICKE SPACES OF SURFACES WITH BOUNDARY
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
The purpose of this paper is to find expressions of the Fricke spaces of some basic surfaces which are a three-holed sphere Σ(0,3), a one-holed torus Σ(1,1), and a four-holed sphere Σ(0,4). For this goal, we define the involutions corresponding to oriented axes of loxodromic elements and an inner product < , > which gives the information about locations of axes of loxodromic elements. The signs of traces of holonomy elements, which are calculated by lifting a representation from PSL(2,C) to SL(2,C), play a very important role in determining the discreteness of holonomy groups.
Abstract
The purpose of this paper is to find expressions of the Fricke spaces of some basic surfaces which are a three-holed sphere Σ(0,3), a one-holed torus Σ(1,1), and a four-holed sphere Σ(0,4). For this goal, we define the involutions corresponding to oriented axes of loxodromic elements and an inner product < , > which gives the information about locations of axes of loxodromic elements. The signs of traces of holonomy elements, which are calculated by lifting a representation from PSL(2,C) to SL(2,C), play a very important role in determining the discreteness of holonomy groups.
참고문헌 (15)
- L. Bers, "Fricke spaces", Adv. in Math, 62(3), pp.249~284 (1986)
- M. Culler, "Lifting representations to covering groups", Adv. in Math, 59(1), pp.64~70 (1986)
- W. Goldman, "The symplectic nature of fundamental groups of surfaces", Adv. in Math, 54(2), pp.200~225 (1984)
- W. Goldman, "Topological components of spaces of representations", Invent. Math, 93(3), pp.557~607 (1988)
- W. Goldman, "Convex real projective structures on compact surfaces", J. Differential Geom, 31(3), pp.791~845 (1990)
- W. Goldman, "Locally homogeneous geometric manifolds", Proceedings of the International Congress of Mathematicians, 2, pp.717~744 (2010), Hindustan Book Agency
- 김홍찬, "Embedding of the Teichm\＂uller space into the Goldman space", 대한수학회지, 43(6), pp.1231~1252 (2006), 대한수학회
- N. Kuiper, "On convex locally projective spaces", Convegno Internazionale di Geometria Differenziale, Italia, 1953, pp.200~213 (1954), Edizioni Cremonese
- W. Magnus, "Rings of Fricke characters and automorphism groups of free groups", Math. Z, 170(1), pp.91~103 (1980)
- K. Matsuzaki, "Hyperbolic Manifolds and Kleinian Groups" (1998), Oxford University Press
- J. Morgan, "Degenerations of hyperbolic structures. III. Actions of 3-manifold groups on trees and Thurston's compactness theorem", Ann. of Math. (2), 127(3), pp.457~519 (1988)
- C. Procesi, "The invariant theory of n × n matrices", Adv. in Math, 19(3), pp.306~381 (1976)
- J. Ratcliffe, "Foundations of Hyperbolic Manifolds" (1994), Springer
- D. Sullivan, "Manifolds with canonical coordinates: some examples", Enseign. Math, 29(1-2), pp.15~25 (1983)
- A. Weil, "On discrete subgroups of Lie groups I", Ann. of Math. (2), 72, pp.369~384 (1960)