Download this article
 Download this article For screen
For printing
Recent Issues

Volume 25
Issue 9, 5175–5754
Issue 8, 4437–5174
Issue 7, 3789–4436
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Meromorphic projective structures: signed spaces, grafting and monodromy

Spandan Ghosh and Subhojoy Gupta

Algebraic & Geometric Topology 25 (2025) 4787–4826
Bibliography
1 D G L Allegretti, Stability conditions, cluster varieties, and Riemann–Hilbert problems from surfaces, Adv. Math. 380 (2021) 107610 MR4205119
2 D G L Allegretti, Stability conditions and Teichmüller space, Math. Ann. 390 (2024) 3827 MR4803465
3 D G L Allegretti, T Bridgeland, The monodromy of meromorphic projective structures, Trans. Amer. Math. Soc. 373 (2020) 6321 MR4155179
4 C L Alley, On the monodromy of meromorphic cyclic opers on the Riemann sphere, Int. Math. Res. Not. 2021 (2021) 16693 MR4338230
5 S Baba, 2π-grafting and complex projective structures, I, Geom. Topol. 19 (2015) 3233 MR3447103
6 S Baba, 2π-grafting and complex projective structures with generic holonomy, Geom. Funct. Anal. 27 (2017) 1017 MR3714716
7 S Baba, On Thurston’s parameterization of P1-structures, from: "In the tradition of Thurston — geometry and topology" (editors K Ohshika, A Papadopoulos), Springer (2020) 241 MR4264579
8 S Baba, Neck-pinching of P1-structures in the PSL2-character variety, J. Topol. 18 (2025) MR4845162
9 M Bainbridge, C Johnson, C Judge, I Park, Haupt’s theorem for strata of abelian differentials, Israel J. Math. 252 (2022) 429 MR4526837
10 S A Ballas, P L Bowers, A Casella, L Ruffoni, Tame and relatively elliptic ℂℙ1-structures on the thrice-punctured sphere, Algebr. Geom. Topol. 24 (2024) 4589 MR4843741
11 F Bonahon, Geodesic laminations on surfaces, from: "Laminations and foliations in dynamics, geometry and topology", Contemp. Math. 269, Amer. Math. Soc. (2001) 1 MR1810534
12 T Bridgeland, I Smith, Quadratic differentials as stability conditions, Publ. Math. Inst. Hautes Études Sci. 121 (2015) 155 MR3349833
13 D Chen, G Faraco, Period realization of meromorphic differentials with prescribed invariants, Forum Math. Sigma 12 (2024) MR4819727
14 S Chenakkod, G Faraco, S Gupta, Translation surfaces and periods of meromorphic differentials, Proc. Lond. Math. Soc. 124 (2022) 478 MR4413502
15 J Danciger, A geometric transition from hyperbolic to anti-de Sitter geometry, Geom. Topol. 17 (2013) 3077 MR3190306
16 D Dumas, Complex projective structures, from: "Handbook of Teichmüller theory, II", IRMA Lect. Math. Theor. Phys. 13, Eur. Math. Soc. (2009) 455 MR2497780
17 D B A Epstein, A Marden, Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces, from: "Analytical and geometric aspects of hyperbolic space", London Math. Soc. Lecture Note Ser. 111, Cambridge Univ. Press (1987) 113 MR903852
18 G Faraco, S Gupta, Monodromy of Schwarzian equations with regular singularities, Geom. Topol. 29 (2025) 549 MR4879364
19 V Fock, A Goncharov, Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci. 103 (2006) 1 MR2233852
20 V V Fock, A B Goncharov, Dual Teichmüller and lamination spaces, from: "Handbook of Teichmüller theory, I", IRMA Lect. Math. Theor. Phys. 11, Eur. Math. Soc. (2007) 647 MR2349682
21 E Frenkel, D Ben-Zvi, Vertex algebras and algebraic curves, 88, Amer. Math. Soc. (2004) MR2082709
22 D Gabai, Almost filling laminations and the connectivity of ending lamination space, Geom. Topol. 13 (2009) 1017 MR2470969
23 D Gallo, M Kapovich, A Marden, The monodromy groups of Schwarzian equations on closed Riemann surfaces, Ann. of Math. 151 (2000) 625 MR1765706
24 W M Goldman, Locally homogeneous geometric manifolds, from: "Proceedings of the International Congress of Mathematicians, II", Hindustan Book Agency (2010) 717 MR2827816
25 S Gupta, Monodromy groups of P1-structures on punctured surfaces, J. Topol. 14 (2021) 538 MR4286048
26 S Gupta, M Mj, Monodromy representations of meromorphic projective structures, Proc. Amer. Math. Soc. 148 (2020) 2069 MR4078090
27 S Gupta, M Mj, Meromorphic projective structures, grafting and the monodromy map, Adv. Math. 383 (2021) 107673 MR4232545
28 A E Hatcher, Measured lamination spaces for surfaces, from the topological viewpoint, Topology Appl. 30 (1988) 63 MR964063
29 O Haupt, Ein Satz über die Abelschen Integrale 1. Gattung, Math. Z. 6 (1920) 219 MR1544406
30 D A Hejhal, Monodromy groups and linearly polymorphic functions, Acta Math. 135 (1975) 1 MR463429
31 D A Hejhal, Monodromy groups for higher-order differential equations, Bull. Amer. Math. Soc. 81 (1975) 590 MR364630
32 D Huybrechts, Complex geometry: an introduction, Springer (2005) MR2093043
33 Y Kamishima, S P Tan, Deformation spaces on geometric structures, from: "Aspects of low-dimensional manifolds", Adv. Stud. Pure Math. 20, Kinokuniya (1992) 263 MR1208313
34 M Kapovich, Periods of abelian differentials and dynamics, from: "Dynamics: topology and numbers" (editors P Moree, A Pohl, L Snoha, T Ward), Contemp. Math. 744, Amer. Math. Soc. (2020) 297 MR4062570
35 R S Kulkarni, U Pinkall, A canonical metric for Möbius structures and its applications, Math. Z. 216 (1994) 89 MR1273468
36 L Lang, Harmonic tropical morphisms and approximation, Math. Ann. 377 (2020) 379 MR4099633
37 S Lang, Algebra, 211, Springer (2002) MR1878556
38 T Le Fils, Periods of abelian differentials with prescribed singularities, Int. Math. Res. Not. 2022 (2022) 5601 MR4406117
39 T Le Fils, Holonomy of complex projective structures on surfaces with prescribed branch data, J. Topol. 16 (2023) 430 MR4575871
40 F Luo, Monodromy groups of projective structures on punctured surfaces, Invent. Math. 111 (1993) 541 MR1202134
41 G Nascimento, Monodromies of projective structures on surface of finite-type, Geom. Dedicata 218 (2024) 1 MR4654135
42 R C Penner, J L Harer, Combinatorics of train tracks, 125, Princeton University Press (1992)
43 H P de Saint-Gervais, Uniformization of Riemann surfaces : revisiting a hundred-year-old theorem, European Mathematical Society (2016) MR3494804
44 T Sérandour, Meromorphic projective structures, opers and monodromy, Int. Math. Res. Not. 2025 (2025) MR4929823
45 Y Sibuya, Global theory of a second order linear ordinary differential equation with a polynomial coefficient, 18, North-Holland (1975) MR486867
46 H Tanigawa, Grafting, harmonic maps and projective structures on surfaces, J. Differential Geom. 47 (1997) 399 MR1617652
47 D Thurston, On geometric intersection of curves in surfaces, unpublished notes