Volume 7, issue 1 (2003)

Download this article
For printing
Recent Issues

Volume 23
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
The modular group action on real $SL(2)$–characters of a one-holed torus

William M Goldman

Geometry & Topology 7 (2003) 443–486
Bibliography
1 W Abikoff, The real analytic theory of Teichmüller space, Lecture Notes in Mathematics 820, Springer (1980) MR590044
2 L Bers, F P Gardiner, Fricke spaces, Adv. in Math. 62 (1986) 249 MR866161
3 B H Bowditch, Markoff triples and quasi–Fuchsian groups, Proc. London Math. Soc. $(3)$ 77 (1998) 697 MR1643429
4 G W Brumfiel, H M Hilden, $\mathrm{SL}(2)$ representations of finitely presented groups, Contemporary Mathematics 187, American Mathematical Society (1995) MR1339764
5 P Buser, Geometry and spectra of compact Riemann surfaces, Progress in Mathematics 106, Birkhäuser (1992) MR1183224
6 M Culler, P B Shalen, Varieties of group representations and splittings of 3–manifolds, Ann. of Math. $(2)$ 117 (1983) 109 MR683804
7 R Feres, Dynamical systems and semisimple groups: an introduction, Cambridge Tracts in Mathematics 126, Cambridge University Press (1998) MR1670703
8 R Fricke, Über die Theorie der automorphen Modulgrupper, Nachr. Akad. Wiss. Göttingen (1896) 91
9 R Fricke, F Klein, Vorlesungen der Automorphen Funktionen I, Teubner (1897)
10 R Fricke, F Klein, Vorlesungen der Automorphen Funktionen II, Teubner (1912)
11 J Gilman, B Maskit, An algorithm for 2–generator Fuchsian groups, Michigan Math. J. 38 (1991) 13 MR1091506
12 W Goldman, Discontinuous groups and the Euler class, PhD thesis, University of California, Berkeley (1980)
13 W M Goldman, Topological components of spaces of representations, Invent. Math. 93 (1988) 557 MR952283
14 W M Goldman, Ergodic theory on moduli spaces, Ann. of Math. $(2)$ 146 (1997) 475 MR1491446
15 W Goldman, An exposition of results of Fricke, in preparation
16 W M Goldman, W D Neumann, Homological action of the modular group on some cubic moduli spaces, Math. Res. Lett. 12 (2005) 575 MR2155233
17 W J Harvey, Spaces of discrete groups, from: "Discrete groups and automorphic functions (Proc. Conf., Cambridge, 1975)", Academic Press (1977) 295 MR0498974
18 R D Horowitz, Induced automorphisms on Fricke characters of free groups, Trans. Amer. Math. Soc. 208 (1975) 41 MR0369540
19 G Kern-Isberner, G Rosenberger, Über Diskretheitsbedingungen und die Diophantische Gleichung $ax^{2}+by^{2}+cz^{2}=dxyz$, Arch. Math. $($Basel$)$ 34 (1980) 481 MR596854
20 Y Imayoshi, M Taniguchi, An introduction to Teichmüller spaces, Springer (1992) MR1215481
21 A Lubotzky, A R Magid, Varieties of representations of finitely generated groups, Mem. Amer. Math. Soc. 58 (1985) MR818915
22 R C Lyndon, P E Schupp, Combinatorial group theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 89, Springer (1977) MR0577064
23 W Magnus, Rings of Fricke characters and automorphism groups of free groups, Math. Z. 170 (1980) 91 MR558891
24 W Magnus, A Karrass, D Solitar, Combinatorial group theory, Dover Publications (2004) MR2109550
25 G A Margulis, Discrete subgroups of semisimple Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 17, Springer (1991) MR1090825
26 R C McOwen, Prescribed curvature and singularities of conformal metrics on Riemann surfaces, J. Math. Anal. Appl. 177 (1993) 287 MR1224820
27 J W Morgan, P B Shalen, Valuations, trees, and degenerations of hyperbolic structures I, Ann. of Math. $(2)$ 120 (1984) 401 MR769158
28 C C Moore, Ergodicity of flows on homogeneous spaces, Amer. J. Math. 88 (1966) 154 MR0193188
29 S Nag, The complex analytic theory of Teichmüller spaces, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons (1988) MR927291
30 J Nielsen, Die Isomorphismen der allgemeinen, unendlichen Gruppe mit zwei Erzeugenden, Math. Ann. 78 (1964) 385 MR1511907
31 J Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, Acta Math. 50 (1927) 189 MR1555256
32 G Stantchev, Dynamics of the modular group acting on $GL(2,\mathbb{R})$–characters of a once-punctured torus, PhD thesis, University of Maryland (2003)
33 J Stillwell, The Dehn–Nielsen theorem, from: "Papers on group theory and topology by Max Dehn", Springer (1987) MR881797
34 M Troyanov, Prescribing curvature on compact surfaces with conical singularities, Trans. Amer. Math. Soc. 324 (1991) 793 MR1005085
35 R J Zimmer, Ergodic theory and semisimple groups, Monographs in Mathematics 81, Birkhäuser Verlag (1984) MR776417