Algebraic & Geometric Topology Volume 25, issue 3 (2025)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Unbounded $\mathfrak{sl}_3$-laminations and their shear coordinates

Tsukasa Ishibashi and Shunsuke Kano

Algebraic & Geometric Topology 25 (2025) 1433–1500

DOI: 10.2140/agt.2025.25.1433

Bibliography

1	D G L Allegretti, Quantization of canonical bases and the quantum symplectic double, Manuscripta Math. 167 (2022) 613 MR4385385
2	D G L Allegretti, H K Kim, A duality map for quantum cluster varieties from surfaces, Adv. Math. 306 (2017) 1164 MR3581328
3	A Berenstein, A Zelevinsky, Quantum cluster algebras, Adv. Math. 195 (2005) 405 MR2146350
4	S Y Cho, H Kim, H K Kim, D Oh, Laurent positivity of quantized canonical bases for quantum cluster varieties from surfaces, Comm. Math. Phys. 373 (2020) 655 MR4056646
5	B Davison, T Mandel, Strong positivity for quantum theta bases of quantum cluster algebras, Invent. Math. 226 (2021) 725 MR4337972
6	D C Douglas, Z Sun, Tropical Fock–Goncharov coordinates for SL₃–webs on surfaces, I : Construction, Forum Math. Sigma 12 (2024) MR4685684
7	D C Douglas, Z Sun, Tropical Fock–Goncharov coordinates for SL₃-webs on surfaces, II : Naturality, Algebr. Comb. 8 (2025) 101 MR4878042
8	V V Fock, L O Chekhov, Quantum Teichmüller spaces, Teoret. Mat. Fiz. 120 (1999) 511 MR1737362
9	V V Fock, A B Goncharov, Cluster 𝒳-varieties, amalgamation, and Poisson–Lie groups, from: "Algebraic geometry and number theory", Progr. Math. 253, Birkhäuser (2006) 27 MR2263192
10	V Fock, A Goncharov, Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci. 103 (2006) 1 MR2233852
11	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
12	V V Fock, A B Goncharov, Moduli spaces of convex projective structures on surfaces, Adv. Math. 208 (2007) 249 MR2304317
13	V V Fock, A B Goncharov, Cluster ensembles, quantization and the dilogarithm, Ann. Sci. École Norm. Sup. 42 (2009) 865 MR2567745
14	V V Fock, A B Goncharov, Cluster Poisson varieties at infinity, Selecta Math. 22 (2016) 2569 MR3573965
15	S Fomin, M Shapiro, D Thurston, Cluster algebras and triangulated surfaces, I : Cluster complexes, Acta Math. 201 (2008) 83 MR2448067
16	S Fomin, A Zelevinsky, Cluster algebras, I : Foundations, J. Amer. Math. Soc. 15 (2002) 497 MR1887642
17	S Fomin, A Zelevinsky, Cluster algebras, IV : Coefficients, Compos. Math. 143 (2007) 112 MR2295199
18	B Fontaine, J Kamnitzer, G Kuperberg, Buildings, spiders, and geometric Satake, Compos. Math. 149 (2013) 1871 MR3133297
19	C Frohman, A S Sikora, SU(3)-skein algebras and webs on surfaces, Math. Z. 300 (2022) 33 MR4359515
20	A Goncharov, L Shen, Donaldson–Thomas transformations of moduli spaces of G-local systems, Adv. Math. 327 (2018) 225 MR3761995
21	A Goncharov, L Shen, Quantum geometry of moduli spaces of local systems and representation theory, preprint (2019) arXiv:1904.10491
22	M Gross, P Hacking, S Keel, M Kontsevich, Canonical bases for cluster algebras, J. Amer. Math. Soc. 31 (2018) 497 MR3758151
23	R Inoue, T Ishibashi, H Oya, Cluster realizations of Weyl groups and higher Teichmüller theory, Selecta Math. 27 (2021) 37 MR4265942
24	T Ishibashi, On a Nielsen–Thurston classification theory for cluster modular groups, Ann. Inst. Fourier (Grenoble) 69 (2019) 515 MR3978318
25	T Ishibashi, S Kano, Sign stability of mapping classes on marked surfaces, I: Empty boundary case, preprint (2020) arXiv:2010.05214
26	T Ishibashi, S Kano, Sign stability of mapping classes on marked surfaces, II: General case via reductions, preprint (2020) arXiv:2011.14320
27	T Ishibashi, S Kano, Algebraic entropy of sign-stable mutation loops, Geom. Dedicata 214 (2021) 79 MR4308270
28	T Ishibashi, S Kano, Unbounded 𝔰𝔩₃-laminations around punctures, preprint (2024) arXiv:2404.18236
29	T Ishibashi, H Oya, L Shen, 𝒜 = 𝒰 for cluster algebras from moduli spaces of G–local systems, Adv. Math. 431 (2023) 109256 MR4631996
30	T Ishibashi, W Yuasa, Skein and cluster algebras of unpunctured surfaces for 𝔰𝔩₃, Math. Z. 303 (2023) 72 MR4552137
31	S Kano, Train track combinatorics and cluster algebras, preprint (2023) arXiv:2303.03190
32	H K Kim, SL₃-laminations as bases for PGL₃ cluster varieties for surfaces, (2020) arXiv:2011.14765
33	G Kuperberg, Spiders for rank 2 Lie algebras, Comm. Math. Phys. 180 (1996) 109 MR1403861
34	I Le, Higher laminations and affine buildings, Geom. Topol. 20 (2016) 1673 MR3523066
35	I Le, Cluster structures on higher Teichmüller spaces for classical groups, Forum Math. Sigma 7 (2019) MR3947634
36	T T Q Lê, T Yu, Quantum traces and embeddings of stated skein algebras into quantum tori, Selecta Math. 28 (2022) 66 MR4431131
37	T Mandel, F Qin, Bracelets bases are theta bases, preprint (2023) arXiv:2301.11101
38	T Nakanishi, Synchronicity phenomenon in cluster patterns, J. Lond. Math. Soc. 103 (2021) 1120 MR4245832
39	A Papadopoulos, R C Penner, The Weil–Petersson symplectic structure at Thurston’s boundary, Trans. Amer. Math. Soc. 335 (1993) 891 MR1089420
40	R C Penner, Decorated Teichmüller theory, Eur. Math. Soc. (2012) MR3052157
41	F Qin, Cluster algebras and their bases, from: "Representations of algebras and related structures", Eur. Math. Soc. (2023) 335 MR4693645
42	D P Thurston, Positive basis for surface skein algebras, Proc. Natl. Acad. Sci. USA 111 (2014) 9725 MR3263305
43	W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417 MR956596
44	T Yurikusa, Acyclic cluster algebras with dense g-vector fans, from: "McKay correspondence, mutation and related topics", Adv. Stud. Pure Math. 88, Math. Soc. Japan (2023) 437 MR4603594