Volume 7, issue 1 (2003)

Download this article
For printing
Recent Issues

Volume 26
Issue 8, 3307–3833
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

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
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
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