Geometry & Topology Volume 28, issue 5 (2024)

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Rigidity and geometricity for surface group actions on the circle

Kathryn Mann and Maxime Wolff

Geometry & Topology 28 (2024) 2345–2398

DOI: 10.2140/gt.2024.28.2345

Bibliography

1	J Alonso, J Brum, C Rivas, Orderings and flexibility of some subgroups of Homeo₊(ℝ), J. Lond. Math. Soc. 95 (2017) 919 MR3664524
2	V A Antonov, Modeling of processes of cyclic evolution type: synchronization by a random signal, Vestnik Leningrad. Univ. Mat. Mekh. Astronom. (1984) 67 MR0756386
3	G Baumslag, On generalised free products, Math. Z. 78 (1962) 423 MR0140562
4	E Breuillard, T Gelander, J Souto, P Storm, Dense embeddings of surface groups, Geom. Topol. 10 (2006) 1373 MR2255501
5	M Burger, A Iozzi, A Wienhard, Higher Teichmüller spaces : from SL(2, ℝ) to other Lie groups, from: "Handbook of Teichmüller theory, IV" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 19, Eur. Math. Soc. (2014) 539 MR3289711
6	D Calegari, A Walker, Ziggurats and rotation numbers, J. Mod. Dyn. 5 (2011) 711 MR2903755
7	A Casson, D Jungreis, Convergence groups and Seifert fibered 3–manifolds, Invent. Math. 118 (1994) 441 MR1296353
8	B Deroin, V Kleptsyn, A Navas, Sur la dynamique unidimensionnelle en régularité intermédiaire, Acta Math. 199 (2007) 199 MR2358052
9	D Eisenbud, U Hirsch, W Neumann, Transverse foliations of Seifert bundles and self-homeomorphism of the circle, Comment. Math. Helv. 56 (1981) 638 MR0656217
10	D Gabai, Convergence groups are Fuchsian groups, Ann. of Math. 136 (1992) 447 MR1189862
11	É Ghys, Classe d’Euler et minimal exceptionnel, Topology 26 (1987) 93 MR0880511
12	É Ghys, Groupes d’homéomorphismes du cercle et cohomologie bornée, from: "The Lefschetz centennial conference, III" (editor A Verjovsky), Contemp. Math. 58, Amer. Math. Soc. (1987) 81 MR0893858
13	É Ghys, Groups acting on the circle, Enseign. Math. 47 (2001) 329 MR1876932
14	W M Goldman, The symplectic nature of fundamental groups of surfaces, Adv. Math. 54 (1984) 200 MR0762512
15	W M Goldman, Topological components of spaces of representations, Invent. Math. 93 (1988) 557 MR0952283
16	W M Goldman, E Z Xia, Ergodicity of mapping class group actions on SU(2)–character varieties, from: "Geometry, rigidity, and group actions" (editors B Farb, D Fisher), Univ. Chicago Press (2011) 591 MR2807844
17	A Hatcher, On triangulations of surfaces, Topology Appl. 40 (1991) 189 MR1123262
18	D Johnson, J J Millson, Deformation spaces associated to compact hyperbolic manifolds, from: "Discrete groups in geometry and analysis" (editor R Howe), Progr. Math. 67, Birkhäuser (1987) 48 MR0900823
19	A Katok, B Hasselblatt, Introduction to the modern theory of dynamical systems, 54, Cambridge Univ. Press (1995) MR1326374
20	S h Kim, T Koberda, M Mj, Flexibility of group actions on the circle, 2231, Springer (2019) MR3887602
21	D Luna, Sur certaines opérations différentiables des groupes de Lie, Amer. J. Math. 97 (1975) 172 MR0364272
22	D Luna, Fonctions différentiables invariantes sous l’opération d’un groupe réductif, Ann. Inst. Fourier (Grenoble) 26 (1976) 33 MR0423398
23	K Mann, Spaces of surface group representations, Invent. Math. 201 (2015) 669 MR3370623
24	K Mann, Rigidity and flexibility of group actions on the circle, from: "Handbook of group actions, IV", Adv. Lect. Math. 41, International (2018) 705 MR3888699
25	K Mann, M Wolff, A characterization of Fuchsian actions by topological rigidity, Pacific J. Math. 302 (2019) 181 MR4028771
26	J Marché, M Wolff, The modular action on PSL₂(ℝ)–characters in genus 2, Duke Math. J. 165 (2016) 371 MR3457677
27	S Matsumoto, Numerical invariants for semiconjugacy of homeomorphisms of the circle, Proc. Amer. Math. Soc. 98 (1986) 163 MR0848896
28	S Matsumoto, Some remarks on foliated S¹ bundles, Invent. Math. 90 (1987) 343 MR0910205
29	S Matsumoto, Basic partitions and combinations of group actions on the circle : a new approach to a theorem of Kathryn Mann, Enseign. Math. 62 (2016) 15 MR3605808
30	J Milnor, On the existence of a connection with curvature zero, Comment. Math. Helv. 32 (1958) 215 MR0095518
31	A Navas, Groups of circle diffeomorphisms, Univ. Chicago Press (2011) MR2809110
32	S Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967) 747 MR0228014
33	D Sullivan, Quasiconformal homeomorphisms and dynamics, II : Structural stability implies hyperbolicity for Kleinian groups, Acta Math. 155 (1985) 243 MR0806415
34	W P Thurston, Earthquakes in two-dimensional hyperbolic geometry, from: "Low-dimensional topology and Kleinian groups" (editor D B A Epstein), Lond. Math. Soc. Lect. Note Ser. 112, Cambridge Univ. Press (1986) 91 MR0903860
35	P Tukia, Homeomorphic conjugates of Fuchsian groups, J. Reine Angew. Math. 391 (1988) 1 MR0961162
36	J W Wood, Bundles with totally disconnected structure group, Comment. Math. Helv. 46 (1971) 257 MR0293655