EMBEDDING OF THE TEICHMULLER SPACE INTO THE GOLDMAN SPACE

Title & Authors
EMBEDDING OF THE TEICHMULLER SPACE INTO THE GOLDMAN SPACE
Kim, Hong-Chan;

Abstract
In this paper we shall explicitly calculate the formula of the algebraic presentation of an embedding of the Teichmiiller space $\small{{\Im}(M)}$ into the Goldman space g(M). From this algebraic presentation, we shall show that the Goldman's length parameter on g(M) is an isometric extension of the Fenchel-Nielsen's length parameter on $\small{{\Im}(M)}$.
Keywords
convex real projective structure;Hilbert metric;Teichmuller space;Goldman space;length parameter;
Language
English
Cited by
1.
INVOLUTIONS AND THE FRICKE SPACES OF SURFACES WITH BOUNDARY,;

대한수학회지, 2014. vol.51. 2, pp.403-426
1.
INVOLUTIONS AND THE FRICKE SPACES OF SURFACES WITH BOUNDARY, Journal of the Korean Mathematical Society, 2014, 51, 2, 403
References
1.
A. F. Beardon, The Geometry of Discrete Groups, Graduate Texts in Mathematics 91, Springer-Verlag, 1983

2.
S. Choi and W. M. Goldman, Convex real projective structures on closed surfaces are closed, Proc. Amer. Math. Soc. 118 (1993), no. 2, 657-661

3.
W. M. Goldman, The symplectic nature of fundamental groups of surfaces, Adv. in Math. 54 (1984), no. 2, 200-225

4.
W. M. Goldman, Geometric structures on manifolds and varieties of representations, Ge- ometry of group representations (Boulder, CO, 1987), 169-198, Contemp. Math., 74, Amer. Math. Soc., Providence, RI, 1988

5.
W. M. Goldman, Convex real projective structures on compact surfaces, J. Differential Geom. 31 (1990), no. 3, 791-845

6.
D. Johnson and J. J. Millson, Deformation spaces associated to compact hyper- bolic manifolds, Discrete groups in geometry and analysis (New Haven, Conn., 1984), 48-106, Progr. Math., 67, Birkhauser Boston, Boston, MA, 1987

7.
H. C. Kim, Matrix presentations of the Teichmuller space of a pair of pants, J. Korean Math. Soc. 42 (2005), no. 3, 553-569

8.
S. Kobayashi, Invariant distances for projective structures, Symposia Mathemat- ica, Vol. XXVI (Rome, 1980), pp. 153-161, Academic Press, London-New York, 1982

9.
N. Kuiper, On convex locally projective spaces, Convegno Int. Geometria Diff., Italy, 1954, 200-213, Edizioni Cremonese, Roma, 1954

10.
K. Matsuzaki and M. Taniguchi, Hyperbolic manifolds and Kleinian groups, Ox- ford Science Publications, Oxford University Press, New York, 1998

11.
J. Ratcliffe, Foundations of hyperbolic manifolds, Graduate Texts in Mathemat- ics, 149. Springer-Verlag, New York, 1994

12.
D. Sullivan and W. Thurston, Manifolds with canonical coordinates charts: some examples, Enseign. Math.(2) 29 (1983), no. 1-2, 15-25

13.
W. Thurston, Three-dimensional geometry and topology. Vol. 1, Princeton Math- ematical Series, 35. Princeton University Press, 1997