Geometry & Topology Volume 15, issue 3 (2011)

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Connected components of the compactification of representation spaces of surface groups

Maxime Wolff

Geometry & Topology 15 (2011) 1225–1295

DOI: 10.2140/gt.2011.15.1225

Bibliography

1	R C Alperin, K N Moss, Complete trees for groups with a real-valued length function, J. London Math. Soc. $(2)$ 31 (1985) 55 MR810562
2	G Baumslag, On generalised free products, Math. Z. 78 (1962) 423 MR0140562
3	R Benedetti, C Petronio, Lectures on hyperbolic geometry, Universitext, Springer (1992) MR1219310
4	M Bestvina, Degenerations of the hyperbolic space, Duke Math. J. 56 (1988) 143 MR932860
5	N Bourbaki, Éléments de mathématique. Topologie générale. Chapitres 1 à 4, Hermann (1971) MR0358652
6	D Calegari, Circular groups, planar groups, and the Euler class, from: "Proceedings of the Casson Fest" (editors C Gordon, Y Rieck), Geom. Topol. Monogr. 7, Geom. Topol. Publ. (2004) 431 MR2172491
7	C Champetier, V Guirardel, Limit groups as limits of free groups, Israel J. Math. 146 (2005) 1 MR2151593
8	M Coornaert, T Delzant, A Papadopoulos, Géométrie et théorie des groupes: les groupes hyperboliques de Gromov, Lecture Notes in Math. 1441, Springer (1990) MR1075994
9	M Culler, P B Shalen, Varieties of group representations and splittings of $3$–manifolds, Ann. of Math. $(2)$ 117 (1983) 109 MR683804
10	J Deblois, R P Kent IV, Surface groups are frequently faithful, Duke Math. J. 131 (2006) 351 MR2219244
11	A Fathi, F Laudenbach, V Poénaru, editors, Travaux de Thurston sur les surfaces, Astérisque 66–67, Soc. Math. France (1979) 284 MR568308
12	J Fresnel, Méthodes modernes en géométrie, Act. Sci. et Ind. 1437, Hermann (1998)
13	L Funar, M Wolff, Non-injective representations of a closed surface group into $\mathrm{PSL}(2,\mathbb R)$, Math. Proc. Cambridge Philos. Soc. 142 (2007) 289 MR2314602
14	É Ghys, Classe d'Euler et minimal exceptionnel, Topology 26 (1987) 93 MR880511
15	É Ghys, Groupes d'homéomorphismes du cercle et cohomologie bornée, from: "The Lefschetz centennial conference, Part III (Mexico City, 1984)" (editor A Verjovsky), Contemp. Math. 58, Amer. Math. Soc. (1987) 81 MR893858
16	É Ghys, Groups acting on the circle, Enseign. Math. $(2)$ 47 (2001) 329 MR1876932
17	É Ghys, P de la Harpe, editors, Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Math. 83, Birkhäuser (1990) MR1086648
18	W M Goldman, Discontinuous groups and the Euler class, PhD thesis, University of California Berkeley (1980)
19	W M Goldman, The symplectic nature of fundamental groups of surfaces, Adv. in Math. 54 (1984) 200 MR762512
20	W M Goldman, Topological components of spaces of representations, Invent. Math. 93 (1988) 557 MR952283
21	V Guirardel, Approximations of stable actions on $\mathbf{R}$–trees, Comment. Math. Helv. 73 (1998) 89 MR1610591
22	V Guirardel, Limit groups and groups acting freely on $\mathbb R^n$–trees, Geom. Topol. 8 (2004) 1427 MR2119301
23	N Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. $(3)$ 55 (1987) 59 MR887284
24	M Kapovich, B Leeb, On asymptotic cones and quasi-isometry classes of fundamental groups of $3$–manifolds, Geom. Funct. Anal. 5 (1995) 582 MR1339818
25	S Katok, Fuchsian groups, Chicago Lectures in Math., Univ. of Chicago Press (1992) MR1177168
26	B Leeb, A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry, Bonner Math. Schriften 326, Univ. Bonn Math. Inst. (2000) arXiv:0903.0584 MR1934160
27	H Masur, Ergodic actions of the mapping class group, Proc. Amer. Math. Soc. 94 (1985) 455 MR787893
28	S Matsumoto, Some remarks on foliated $S^1$ bundles, Invent. Math. 90 (1987) 343 MR910205
29	C T McMullen, Ribbon $\mathbb R$–trees and holomorphic dynamics on the unit disk, J. Topol. 2 (2009) 23 MR2499437
30	J Milnor, On the existence of a connection with curvature zero, Comment. Math. Helv. 32 (1958) 215 MR0095518
31	J W Morgan, Group actions on trees and the compactification of the space of classes of $\mathrm{SO}(n,1)$–representations, Topology 25 (1986) 1 MR836721
32	J W Morgan, P B Shalen, Valuations, trees, and degenerations of hyperbolic structures. I, Ann. of Math. $(2)$ 120 (1984) 401 MR769158
33	A Parreau, Compactification d'espaces de représentations de groupes de type fini, preprint (2010)
34	A Parreau, Espaces de représentations complètement réductibles, J. London Math. Soc. 83 (2011) 545
35	F Paulin, Topologie de Gromov équivariante, structures hyperboliques et arbres réels, Invent. Math. 94 (1988) 53 MR958589
36	F Paulin, The Gromov topology on $\mathbf{R}$–trees, Topology Appl. 32 (1989) 197 MR1007101
37	F Paulin, Sur la compactification de Thurston de l'espace de Teichmüller, from: "Géométries à courbure négative ou nulle, groupes discrets et rigidités" (editors L Bessières, A Parreau, B Rémy), Sémin. Congr. 18, Soc. Math. France (2009) 421 MR2655319
38	V Poénaru, Groupes discrets, Lecture Notes in Math. 421, Springer (1974) MR0407155
39	Z Sela, Diophantine geometry over groups. I: Makanin–Razborov diagrams, Publ. Math. Inst. Hautes Études Sci. 93 (2001) 31 MR1863735
40	R K Skora, Splittings of surfaces, J. Amer. Math. Soc. 9 (1996) 605 MR1339846
41	W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. $($N.S.$)$ 19 (1988) 417 MR956596
42	A Weil, Remarks on the cohomology of groups, Ann. of Math. $(2)$ 80 (1964) 149 MR0169956
43	M Wolff, Sur les composantes exotiques des espaces d'actions de groupes de surfaces sur le plan hyperbolique, PhD thesis, Université de Grenoble I (2007)
44	J W Wood, Bundles with totally disconnected structure group, Comment. Math. Helv. 46 (1971) 257 MR0293655