Algebraic & Geometric Topology Volume 24, issue 8 (2024)

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Tame and relatively elliptic $\mathbb{CP}^1$–structures on the thrice-punctured sphere

Samuel A Ballas, Philip L Bowers, Alex Casella and Lorenzo Ruffoni

Algebraic & Geometric Topology 24 (2024) 4589–4650

DOI: 10.2140/agt.2024.24.4589

Bibliography

1	D G L Allegretti, T Bridgeland, The monodromy of meromorphic projective structures, Trans. Amer. Math. Soc. 373 (2020) 6321 MR4155179
2	S Baba, A Schottky decomposition theorem for complex projective structures, Geom. Topol. 14 (2010) 117 MR2578302
3	S Baba, Complex projective structures with Schottky holonomy, Geom. Funct. Anal. 22 (2012) 267 MR2929066
4	S Baba, 2π–grafting and complex projective structures, I, Geom. Topol. 19 (2015) 3233 MR3447103
5	S Baba, 2π–grafting and complex projective structures with generic holonomy, Geom. Funct. Anal. 27 (2017) 1017 MR3714716
6	S Baba, On Thurston’s parameterization of ℂP¹–structures, from: "In the tradition of Thurston—geometry and topology" (editors K Ohshika, A Papadopoulos), Springer (2020) 241 MR4264579
7	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
8	G Calsamiglia, B Deroin, S Francaviglia, Branched projective structures with Fuchsian holonomy, Geom. Topol. 18 (2014) 379 MR3159165
9	G Calsamiglia, B Deroin, S Francaviglia, The oriented graph of multi-graftings in the Fuchsian case, Publ. Mat. 58 (2014) 31 MR3161507
10	G Calsamiglia, B Deroin, V Heu, F Loray, The Riemann–Hilbert mapping for 𝔰𝔩₂ systems over genus two curves, Bull. Soc. Math. France 147 (2019) 159 MR3943741
11	S Chenakkod, G Faraco, S Gupta, Translation surfaces and periods of meromorphic differentials, Proc. Lond. Math. Soc. 124 (2022) 478 MR4413502
12	B Deroin, R Dujardin, Complex projective structures : Lyapunov exponent, degree, and harmonic measure, Duke Math. J. 166 (2017) 2643 MR3707286
13	D Dumas, Complex projective structures, from: "Handbook of Teichmüller theory, II" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 13, Eur. Math. Soc. (2009) 455 MR2497780
14	A Eremenko, Metrics of positive curvature with conic singularities on the sphere, Proc. Amer. Math. Soc. 132 (2004) 3349 MR2073312
15	G Faraco, Distances on the moduli space of complex projective structures, Expo. Math. 38 (2020) 407 MR4177950
16	G Faraco, L Ruffoni, Complex projective structures with maximal number of Möbius transformations, Math. Nachr. 292 (2019) 1260 MR3959460
17	S Francaviglia, L Ruffoni, Local deformations of branched projective structures : Schiffer variations and the Teichmüller map, Geom. Dedicata 214 (2021) 21 MR4308267
18	D Gallo, M Kapovich, A Marden, The monodromy groups of Schwarzian equations on closed Riemann surfaces, Ann. of Math. 151 (2000) 625 MR1765706
19	W M Goldman, Projective structures with Fuchsian holonomy, J. Differential Geom. 25 (1987) 297 MR882826
20	R C Gunning, Special coordinate coverings of Riemann surfaces, Math. Ann. 170 (1967) 67 MR207978
21	S Gupta, Monodromy groups of ℂP¹–structures on punctured surfaces, J. Topol. 14 (2021) 538 MR4286048
22	S Gupta, M Mj, Monodromy representations of meromorphic projective structures, Proc. Amer. Math. Soc. 148 (2020) 2069 MR4078090
23	S Gupta, M Mj, Meromorphic projective structures, grafting and the monodromy map, Adv. Math. 383 (2021) 107673 MR4232545
24	D A Hejhal, Monodromy groups and linearly polymorphic functions, Acta Math. 135 (1975) 1 MR463429
25	S W Hensel, Iterated grafting and holonomy lifts of Teichmüller space, Geom. Dedicata 155 (2011) 31 MR2863893
26	M Heusener, J Porti, The variety of characters in PSL₂(ℂ), Bol. Soc. Mat. Mexicana 10 (2004) 221 MR2199350
27	E Hille, Lectures on ordinary differential equations, Addison-Wesley (1969) MR249698
28	N Hussenot Desenonges, Heijal’s theorem for projective structures on surfaces with parabolic punctures, Geom. Dedicata 200 (2019) 93 MR3956187
29	E L Ince, Ordinary differential equations, Dover (1944) MR10757
30	Y Kamishima, S P Tan, Deformation spaces on geometric structures, from: "Aspects of low-dimensional manifolds" (editors Y Matsumoto, S Morita), Adv. Stud. Pure Math. 20, Kinokuniya (1992) 263 MR1208313
31	M Kapovich, Periods of abelian differentials and dynamics, from: "Dynamics: topology and numbers" (editors P Moree, A Pohl, Ľ Snoha, T Ward), Contemp. Math. 744, Amer. Math. Soc. (2020) 297 MR4062570
32	I Kra, Deformations of Fuchsian groups, Duke Math. J. 36 (1969) 537 MR265582
33	I Kra, Deformations of Fuchsian groups, II, Duke Math. J. 38 (1971) 499 MR285734
34	I Kra, A generalization of a theorem of Poincaré, Proc. Amer. Math. Soc. 27 (1971) 299 MR301189
35	R S Kulkarni, U Pinkall, A canonical metric for Möbius structures and its applications, Math. Z. 216 (1994) 89 MR1273468
36	F Luo, Monodromy groups of projective structures on punctured surfaces, Invent. Math. 111 (1993) 541 MR1202134
37	R Mandelbaum, Branched structures on Riemann surfaces, Trans. Amer. Math. Soc. 163 (1972) 261 MR288253
38	B Maskit, On a class of Kleinian groups, Ann. Acad. Sci. Fenn. Ser. A I 442 (1969) 8 MR252638
39	G Mondello, D Panov, Spherical metrics with conical singularities on a 2–sphere : angle constraints, Int. Math. Res. Not. 2016 (2016) 4937 MR3556430
40	H Poincaré, Sur l’uniformisation des fonctions analytiques, Acta Math. 31 (1908) 1 MR1555036
41	J G Ratcliffe, Foundations of hyperbolic manifolds, 149, Springer (2006) MR2249478
42	L Ruffoni, Multi(de)grafting quasi-Fuchsian complex projective structures via bubbles, Differential Geom. Appl. 64 (2019) 158 MR3921239
43	L Ruffoni, Bubbling complex projective structures with quasi-Fuchsian holonomy, J. Topol. Anal. 13 (2021) 843 MR4312457
44	K Strebel, Quadratic differentials, 5, Springer (1984) MR743423